You could start by being less of a total nerd.
I have a feeling that you're putting too much pressure on yourself to come up with the "right" line. Wit and humor are best when they're spontaneous, and those people aren't putting pressure on themselves to be funny. It happens because their mind is free to move into areas of linguistic and situation absurdity. You can't demand yourself to produce something like that because you can't demand that you produce anything natural. So, you really have to be in the right mood, and self-critical or judgmental (same thing, different orientation) is not the right mood.
So, what should you do? I say forget trying to be a funny person and focus on laughing and loosening up. Start to broaden your comedic palette by searching out new comedians and new forms of comedy (physical, slapstick, situational). If you demand yourself to like it, well, obviously, you won't, because you won't be in the right mood (back to self-critical). If you've already set some parameters about what humor tickles you, you also won't enjoy it because you'll be too discriminating (back to judgmental). If you just give a chance, who knows. Maybe it'll suck, but maybe you'll find its extreme suckage to be amusing.
YouTube and ComedyCentral might be some places to start. Renting some movies, watching some shows (Curb Your Enthusiasm), cartoons maybe (Family Guy), too. (I don't like modern sitcoms either, by the way.)