I just installed my new vanity top without any trouble. When I went to re-connect the pipes under the sink, I encountered a problem. For some reason (the new sink is basically in the same position as the old one was), the trap doesn't fit now. It's about 1/2 inch away from the pipe that drains into the wall. I tried forcing it, but I'm afraid I am going to crack the drain pipe that comes down from my new sink. It's like a puzzle and I can't think it through. Anyone out that that knows how to make this work. Thank You very much.

1/2" away, which way left, right, up or down? It could be your new traps tail piece needs to be cut shorter to raise it up.

You might need to find another type of trap fitting that will allow for more flexibility in the positioning? The type I am thinking of has connections at both ends and looks like a U or maybe two J type fittings?

That thing that looks like a U is the P trap and I think Herman is talking about the next piece in the system, the lateral to the wall.