Kay, so first, you need to write a letter to your Clan, kind of like the Medicine Cat letter you wrote when you first became a Med. Cat, and post it in the Medicine Cat Den Thread thing on the ThunderClan board, telling your Clan that you're becoming a loner.
Next, think of a new, loner-ish name (or you can keep your Clan name -- whichever you want) and PM Moonstar, asking her to change your name. Your title will also be changed from "ThunderClan Medicine Cat" to "Loner," which I will do in a bit.
Finally, you may make a loner den thread for yourself, though this is not required. For an example of one, just check out either mine, or someone elses (no one comes to mind, ATM. =/ )
And that's pretty much it.
And, just so you know, I'm going off of what I've seen; I'm not completely sure if the letter thing is required, but just in case...