The least you can do is probably not use hosted wallets. They are not actual bitcoin wallets where you control your own private keys, which means that the hosted wallet provider like coinbase is likely to be able to see all your transactions both in an out.

Also, don't reuse addresses in your wallet. Most wallets already do this automatically.

If you're really savvy about your privacy, then potentially using a mixer could obscure your tracks as well. Most of the times, though, it's going to be far more efficient to just use a normal, desktop wallet which you have full control over your privkeys with, that should be sufficient anonymity unless you suspect someone's monitoring you.