I am installing a new pipe in my bathroom sink. I thought I had everything attatched correctly, but water does not exit the pipes. The pipes are NOT clogged. Can you help me?

May need more details before anybody can help. New pipes? Tail stock, runs from the hole in the sink straight down. P trap, U shaped goes from tail to wall pipe. Wall pipe, L shaped goes from P trap back inside the wall to a tee. The tee is very important, allowing the water to go down the drain and air to pushed out of the way or pulled back in as needed. Which pipes did you replace, and where does the water stand? Was it working before?

I replaced the tail I guess, but that's not the problem. It's the other two I think. THey don't drain out to the hole in the wall. Could it be the seal, or does that matter? Could it be the angle? I don't get it, but each time I test the pipes after refitting them, the water goes down and then it begins to back up into the sink.

"THey don't drain out to the hole in the wall."
And with those words you just told me that you had a blockage in the lateral (horizontal) arm inside the wall. Remove the "J"bend from the trap and send a snake up into the wall. You will hit a elbo about 6" in but crank and work your way around it for about 5 more feet. Reassemble and run hot water down the drain to flush out the line. Good luck, tom