step 1 - memorize all the private keys that would otherwise be stored in some sort of wallet file

step 2 - there is no step 2

You can use http://brainwallet.org to generate a so-called "Memory Wallet". Do not use the live website, download the sourcecode from github.

How this works is you select a phrase, like "Correct Horse Battery Staple", and that phrase will consistently compute to a keypair you can use to store and later retrieve bitcoins.

BE EXTREMELY CAREFUL, or maybe don't do this at all. There are untold numbers of robots perpetually checking the blockchain for any conceivable passphrase. If your passphrase is not EXTREMELY strong, any coins you put in there will likely be swiped in a matter of hours, if not minutes.

See: http://www.reddit.com/r/Bitcoin/comments/1ndsxi/a_test_of_brainwallet_passphrases/

If you really want to make a brain wallet, I recommend something absolutely impossible to brute force, like

my favorite superhero, childhood address, my social security number

giving you

Captain Underpants, 112 Elm Street, Oakland, CA, 555-1212-555

This is most secure way to place your Bitcoins in cold storage.

This quick Video Tutorial explains how to make a Dr. Evil Paper Wallet or Bitcoin "Brain Wallet."

Get the ZIP file for Dr Evil Paper Wallet Generator @GitHub
https://github.com/obesityspray/Dr.-Evil-Paper-Wallet

Well, the brain wallet is essentially the mnemonic.

You can try using the BIP 39 tool. But keep in mind to save the code from Github and run it while Offline. Preferrably in a Tails OS or some disposable system/hardware (one can never be too paranoid).

After that, just keep those words in your head. When you need to interact with the wallet you download some standard wallet and while on setup, hit "recover" and insert the mnemonic that is in your brain.