Instructions for safely splitting your BCH from your BTC

Here are general split instructions. If your wallet software gives different instructions, use those instead.

These are the best instructions I could come up with quickly. Maybe someone will eventually come up with a more convenient way of doing it. Note that while I believe these instructions to be safe and reasonable, you are solely responsible for your safety here.

 1. Decide whether you want to bother splitting your coins at all. Is it actually worthwhile to remove your coins from cold storage (or whatever)? If you take no particular action and continue using Bitcoin as normal, then your BCH is likely (but not guaranteed) to remain associated with the current private keys due to BCH's pseudo-replay-protection; you could therefore maybe claim your BCH later on if you want. If you want to claim your BCH now, continue to the next steps.
 2. Create a totally new logical wallet with a new mnemonic, etc. Just creating new addresses is not sufficient: the new wallet needs to be completely separate from the old one. The new wallet's private keys should be under your personal control just in case your transaction is replayed or something else goes wrong. Make sure you have backups of the new wallet.
 3. Send all of the BTC in your old wallet to your new wallet, and wait until this transaction has 30 confirmations. (If you are really itching to get your BCH, it would not be totally crazy to wait for as few as 3 confirmations, but there is some risk with that.) Note that sending all of your BTC in a single transaction is likely to be harmful to your privacy; if you care about this, you might want to send it in several smaller transactions to several different addresses on the new wallet.
 4. On a separate computer that you wouldn't too much mind being compromised, install a BCash wallet such as one of the ones listed on bitcoincash.org. (Warning: some Bcash wallets are known to overwrite important files belonging to their Bitcoin counterparts.) Or use a Web-based exchange/wallet supporting Bcash. Import the private keys from your old, now-empty Bitcoin wallet into this Bcash wallet. Now you have BCH which you can handle as you wish. Note that BCH transactions may be very slow to confirm for a couple of days.