Go to options, AutoText, then press the BB button, select new. Where it says "replace" type in ZZ. And where it says "with", type in your signature. Now save and exit. Now go to your SMS, type your message. at the end of your message, type in ZZ and space. Your new signature will now be displayed.
There is also a really cheap small app you can get called "Smart Sig".
Not only does it append a signature to your text messages, you can also manage your email signatures right from your BB and not your carrier's BIS page. Much easier. That's why I got it.
If it's 1:1 communication, why bother with a signature? That's like referring to yourself in the third person, and writing your name on all your stuff if you have one roommate.