I have thought about this a while and found this article that seemed interesting and is quite on point.
The sentence this whole article starts off with is "Take responsibility for your privacy." and is that so true!
Newbies come into Bitcoin thinking is all private and untraceable... not really...
Bitcoin is less private than cash, yet more private than a credit card.

The first thing to make it not anonymous is the Blockchain which is both Public and Permanent
Bitcoin is pseudonymous, not anonymous.
This means that you are operating under another identity and different transactions that you make can be tied to that identity

A smart thing is:
A Bitcoin Address is like an email address.  You can have as many email addresses as you want.  However, once someone ties your real identity to your email address, then they know that every email ever sent from that email address came from you. 

Please weigh in if these steps are wrong or you don't agree!


The steps:

1. Assume your transactions are not anonymous.
Do not assume your transactions are private.  The most private transactions are the transactions which never occur. 

2. Maintain different wallets, passphrases, and accounts.
Remove the links between your bitcoin addresses.  If you receive bitcoin from many sources, and spend them in the same transaction, your bitcoin addresses will be linked together in that transaction.
Instead, keep a separate accounts for saving and spending. 

3. Acquire bitcoin from friends and customers.
The most anonymous way to acquire bitcoin is to buy it from a stranger, in person, for cash.  However, this may be dangerous. 
Instead, try to buy bitcoin from a friend.  Alternatively, try to earn bitcoin by selling goods or services for it.

4. Coinjoin your Bitcoin – “the money laundering of Bitcoin”
Coin-join is a type of bitcoin transaction which creates fresh bitcoin, without a clear transaction history.
Imagine if many people each put a dollar into a hat, and randomly took a dollar out of the hat.  Then, they would each have a dollar that came from someone else.  That is the idea behind a coin-join. Coin-joining is legal, but helping another person evade law enforcement is not legal.

5. Send and receive bitcoins from a Bitcoin Core wallet. 
The most private way to obtain information from the blockchain is to verify and download the blockchain yourself.  Otherwise, you are asking someone else to check the blockchain for you.  They will know your IP address, when you asked, and which records you are requesting.

6. Use Tails operating system Live Boot USB
Tor allows you to access the internet anonymously.  Tor sends encrypted messages to many random computers, which anonymously forward the message until it reaches its destination. 

Please see link for full article, which explains it in more context.

Source and Full Article:
https://thebitcoinchain.com/how-to-be-anonymous-when-using-bitcoin-7-steps/