Using CoinJoin increases your privacy but you have to read rules of platforms before sending your funds to them. Platforms tend to restrict CoinJoin transactions.
Only use Coin Join transactions if you have fully control.
Avoid using Coin Join transactions on third-party platforms that don't allow it.^[e].

"Not your keys, not your bitcoin" ^[3]
It is a vital rule, so if one want to enhance privacy, s/he should learn to use non-custodial wallets that provide enhanced privacy, like Wasabi and Samourai. There are so many mixing platforms but it is risky to store your coins too long on those platforms. Someone made that mistake and lose their coins on scam mixing platforms.

There are two wallets for this purpose:

Wasabi wallet
Samourai wallet

They are both use Coinjoin to give users modification options to enhance their privacy.

It is worth to warn you all that those wallets only enhance your privacy, and not give your completely privacy. Additionally, the personal practice of user will determine level of privacy they have.

Now, let's see what is Coinjoin

CoinJoin: Bitcoin privacy for the real world
CoinJoin is a trustless method for combining multiple Bitcoin payments from multiple spenders into a single transaction to make it more difficult for outside parties to determine which spender paid which recipient or recipients. Unlike many other privacy solutions, coinjoin transactions do not require a modification to the bitcoin protocol. ^[1]
In very simple terms, coinjoin means: when you want to make a transaction, find someone else who also wants to make a transaction and make a joint transaction together. ^[2]

Wasabi wallet
Wasabi Wallet 1.0 Is Released
Website: https://wasabiwallet.io/
FAQs

Why Wasabi ?

Quote from: https://docs.wasabiwallet.io/why-wasabi/

Wasabi Wallet is an open source, non-custodial, privacy-focused, desktop Bitcoin wallet offered by zkSNACKs Ltd. It differentiates itself from many other wallets for its strong focus on user privacy.

Quote from: theymos on May 22, 2019, 10:18:50 PM

#1 - Wasabi wallet

The Wasabi wallet uses CoinJoin in order to anonymize BTC.

- Pros: Easy to use; fairly cheap ~0.15% fee; pretty good privacy; automatically uses Tor
- Cons: ~0.1BTC minimum; with a great deal of effort and investigation, transaction analysis may still be possible, especially if you leave other traces; the coordinator could possibly do an active sybil attack against specific coins

Wasabi wallet has processed 5372 Coinjoin transactions as of writing

What's the legal status of Wasabi/CoinJoin? ^[5]
USA: On May 9, 2019, the Financial Crimes Enforcement Network (FinCEN) issued an interpretive guidance that stated the following in section 4.5.1(b):

Quote

An anonymizing software provider is not a money transmitter. FinCEN regulations exempt from the definition of money transmitter those persons providing "the delivery, communication, or network access services used by a money transmitter to support money transmission services."

Wasabi is an Anonymizing software provider so it is not a money transmitter, thus not under Bank Secrecy Act (BSA) regulations. Basically we can continue to operate like now and it is compliant.

Anonymity sets
What is anonymity set?
The anonymity set is effectively the size of the group you are hiding in. ^[4]

Quote from: https://wasabiwallet.io/#faq

If 3 people take part in a CoinJoin (with equal size inputs) and there are 3 outputs then each of those output coins has an anonymity set of 3.

There is no way to know which of the anon set output coins are owned by which of the input owners. All an observer knows is that a specific anon set output coin is owned by one of the owners of one of the input Coins i.e. 3 people - hence an anonymity set of 3.

Your Wasabi software has limited information on what the anonymity set should be, so the anonymity set that the software presents you is just an estimation, not an accurate value. With Wasabi we are trying to do lower estimations, rather than higher ones.

Quote from: theymos on May 22, 2019, 10:18:50 PM

Both Wasabi and Monero can be thought of in terms of "anonymity sets". If you're spending some BTC with an anonymity set of 50, this means that an observer can see that the sender is one of 50 people, but they can't tell which. So someone investigating a particular transaction you sent would have you "in their sights" to a certain extent from the start since you're among the 50, but in order to prove that you sent it, they'd have to either eliminate 49 other people from consideration or find some other evidence linking you to it.

Wasabi always aims for an anonymity set of 50 when mixing. Monero has an anonymity set of 11 per transaction. If you cascade transactions as I suggest above, then this multiplies, so after two transactions you have an anonymity set of 11*11=121, and after a cascade of three you'd have an anonymity set of 1331.

The quality of each member in the anonymity set isn't quite comparable, though. Monero is able to hide transaction amounts, which is helpful, but I tend to consider the quality of Monero anonymity-set-members to be lower on average, since many are probably owned by hosted wallets or other possible global adversaries.

See also

https://en.bitcoin.it/wiki/Privacy

Fees for Coinjoins

Quote

You currently pay a fee of 0.003% * anonymity set. If the anonymity set of a coin is 50 then you pay 0.003% * 50 (=0.15%). If you set the target anonymity set to 53 then Wasabi will continue mixing until this is reached, so you may end up with an anonymity set of say 60, and you will pay 0.003% * 60 (=0.18%).

There are also edge cases where you do not pay the full fee or where you pay more. For example if you're the smallest registrant to a round, you will never pay a fee. Also when you are remixing and you cannot pay the full fee with your input, then you only pay as much as you have, but if the change amount leftover would be too small, then that is also added to the fee. Currently the minimum change amount to be paid out is 0.7% of the base denomination (~0.1BTC.)

It is also possible that you get more back from mixing than you put in. This happens when network fees go down between the start of the round and its end. In this case, the difference is split between the active outputs of the mix.

Avoid to recombine mixed coins

Quote

It is advisable to limit the recombining of mixed coins because it can only decrease the privacy of said coins. This links all the consolidated UTXOs in one transaction, creating only one output, which then clearly controls all these funds. That said, if you combine less than 1 BTC it is less likely to reveal your pre-coinjoin transaction history. The potential issue comes when you spend that coin. Depending on what you do with the coin you might reduce the privacy of the resulting change (if you send half your coin to an exchange for example, as they will know that you own the coin change). As a result it is best not to recombine ALL your mixed change, though you may wish to recombine some coins if you are planning on hodling for many years as this will reduce the fees required to spend the coins later.

More guides on Recombine mixed coins

Verify first, before installing
It is the same rule with other wallets, verifing package first before installing (if wallets have that option).

Quote from: https://docs.wasabiwallet.io/using-wasabi/InstallPackage.html

It is strongly recommended to VERIFY PGP SIGNATURES of the downloaded packages before installing Wasabi. This protects you against malicious phishing sites giving you back-doored Wallet software. Don't trust - Verify!

There are different wallets, for: MacOs, Windows, Linux, Ubuntu / Debian. Download here

How to install?
Install Instruction
Youtube guide

Choose other Bench32-support wallets that have coin control features
Wasabi wallet only supports to generate Bench32 address, but it does not support to send your bitcoin to others Bench32-address, so you have to choose other alternative wallets to do this.
Suggested wallets ^[4]:

Mobile (Android): Samourai, ~~Electrum~~
Desktop: Bitcoin Core, Electrum

Read more: Why does Wasabi only use SegWit bech32 addresses?

Some notes on Wasabi wallet

Wasabi wallet implement bitcoin transactions through Coinjoin inputs and Coinjoin outputs, but the wallet is unable to know which outputs of belong to which inputs. This is why it brings more privacy to users.
Practice of coin control after mixing will identify the level of privacy users have. That depends on practice of users, not the Wasabi wallet.
Wasabi wallet uses Tor by default, and users don't have to set up Tor. ^a

Do not turn off Tor in Settings, because it might damage their privacy by IP address.
Verify first, before installing
Wasabi wallet only generate Bench32 address (with prefix bc1 at the start of address), but unable to send BTC to other Bench32 address
Don't send all of your bitcoins to a new wallet, instead import your seeds into new wallet in order to protect your privacy.

^a

Quote from: https://wasabiwallet.io/#faq

All Wasabi network traffic goes via Tor by default - no need to set up Tor yourself. If you do already have Tor, and it is running, then Wasabi will try to use that first.

You can turn off Tor in the Settings. Note that in this case you are still private, except when you coinjoin and when you broadcast a transaction. In the first case, the coordinator would know the links between your inputs and outputs based on your IP address. In the second case, if you happen to broadcast a transaction of yours to a full node that is spying on you, it will know the link between your transaction and your IP address.

Samourai wallet
It is important to note that at beginning, lead developers of Wasabi and Samourai wallets worked together to build one application, then their vision to develop diverged and they splited to develop different wallets. From that, we have Wasabi and Samourai wallets.

Read more there: https://www.coindesk.com/a-battle-between-bitcoin-wallets-has-big-implications-for-privacy

Website: https://samouraiwallet.com
Download: https://samouraiwallet.com/download
Blog: https://blog.samouraiwallet.com/
Twitter: https://twitter.com/samouraiwallet
Support: https://samouraiwallet.com/support

There are so many different features with Samourai wallet, from there you can have a quick comparison between them. Please click on Details link to see detail explanation of each feature.

DOJO
Among them, Dojo is the one that makes Samourai wallet is different and help users conveniently and easily to set up their Bitcoin full nodes.

Offline
With Samourai wallet, users can easily switch between online and offline mode to use their bitcoins. That is an amazing feature from Samourai.

References:
^[1] https://en.bitcoin.it/wiki/CoinJoin
^[2] https://wasabiwallet.io/
^[3] https://docs.wasabiwallet.io/
^[4] https://wasabiwallet.io/#faq
^[5] https://docs.wasabiwallet.io/FAQ/FAQ-UseWasabi.html#what-s-the-legal-status-of-wasabi-coinjoin

Wasabi developer
https://medium.com/@nopara73
https://twitter.com/nopara73?lang=en[/list]

Theymos' opinion on privacy
[1] [Guide] Decent mixing methods (on Wasabi-CoinJoin and Monero)

[2] Technically aspects of Monero, Grin and potential for future developments

Quote from: theymos on November 20, 2019, 01:07:32 AM

Quote from: DdmrDdmr on November 19, 2019, 08:42:41 AM

Relating to Mimblewimble and Grin, Ive come across a couple of recent interesting reads, fresh from the oven:

https://medium.com/dragonfly-research/breaking-mimblewimble-privacy-model-84bcd67bfe52
https://medium.com/grin-mimblewimble/factual-inaccuracies-of-breaking-mimblewimbles-privacy-model-8063371839b9 (counters arguments to the former link).

I dont really know how much certainty the above articles provide, but it casts some doubt as to exactly how far the anonymity goes. At least if its what I was after, Id keep reading these sort of articles for a few days to get a better idea of the extent.

AFAIK, that medium post is nothing new.

Base mimblewimble isn't really designed to be a "black box of reliable anonymity" in the way that Monero or Wasabi-CoinJoins are, where connections are hard-broken. It's more of a framework on which you could build solid anonymity using techniques that have largely not yet been perfected, plus major scaling benefits. Monero = CT + stealth addresses + ring signatures. Grin = CT + "stealth addresses" + mimblewimble. Because grin replaces ring signatures with mimblewimble, its privacy is less reliable than Monero's. Probably the grin developers have tried to make their mimblewimble transaction aggregation methods good, but I currently wouldn't put much faith in it, and IMO it'll take many years of research to get something really solid. That said, CT + stealth addresses offer a certain base level of privacy, and grin's method of handling stealth addresses (using an interactive protocol, exchanging "slates") is both more scalable than Monero and probably more private.

If your goal is to mix coins, grin is definitely not for you right now, and it may never be. Monero's goal is maximal privacy, regardless of the cost. Grin's goal is excellent privacy, consistent with scaling.

^[e]: