...Does the move Absorb work!? Do they shoot out a vine that sucks the life from the enemy!? Same goes for drain punch. I understand Leech Life, and Dream eater, but does anyone have any Ideas how absorb works? I've never seen it in the show.

Well, in the show, there's some instances:

Absorb: Well, there was Giga Drain, which works just about the same way as Absorb. I think it, as you said, shoots a vine out, injects itself into the opponent, and sucks their life.

Drain Punch: One of Maylene's Pokemon used it (I forget which one) and I believe that the fist acts like a leech or something.

That's just how it seems to me. It may not be accurate.

Its a special move so the show fails to portray it accurately. Absorb works by sucking energy like dream eater; instead of touching the opponent to suck energy; that is, you absorb their energy through indirect means (can't really explain it any better).

im guessing its like, the move drains energy from an opponent, which is then manifested in a ball of energy, which is then sent into the user. with moves like leech seed and drain punch, i guess the energy just travels through the fist or vine