http://i.imgur.com/Hyvqrvg.png
http://i.imgur.com/7pSK5Ux.png
In the first picture you can see its missing a piece that broke which in the second picture is of that piece on my other sink. I went out to buy a replacement for it already but this is where the problem is and that is the tailpiece on the first picture where the arrow is pointing to is stuck in that P-trap. Ive looked online for replacing those parts and it only mentions to unscrew that white piece that secures the tailpiece. Even after I unscrew it the tailpiece is still stuck hard in there no matter what I try to pull it out.

Use your pliers and grab the tailpiece and spin it around a few times... should loosen it. If that fails to fix the issue, remove the strainer and pull up on the tailpiece while spinning the tailpiece... that should get it out. If you damage the tailpiece pick up a plastic one and reuse the strainer washer. Sometimes, these can be a little tough to get started, but the tailpiece should eventually loosen pretty easily.

Mark

Aside from Mark's excellent advice: that 1 1/2" ABS black drain pipe should flexible and move left and right a bit. Push it one way to by-pass the strainer - and pull out the tail piece

If the ABS pipe doesn't move, than you can also cut it in the horizontal section, remove tail-piece, insert new one ( don't forget to insert the white nut onto the tail piece first ) - and glue the same pipe back together using ABS coupling and ABS glue.

If you don't want to mess with glue, than you can use Fernco Flex / rubber coupling. This coupling comes with two s.s. bands that you tighten up with screwdriver. This coupling is removable and reusable. You can purchase one in Home Depot for about $4.00

Hope that helps

Milo