And maybe a new tail piece - the straight pipe exiting the drain assembly.
It should be relatively easy for you to change out. The baskets run from, IIRC, 12 bucks for a cheap one to 40 bucks for a better quality Kohler at Home Depot.
See this video for an idea of what you are dealing with:
http://www.youtube.com/watch?v=sY5IFLmjtJ0http://www.youtube.com/watch?v=K3tB34H-Q84This one goes in to more detail in the event you desire/need to change some or all the pipe underneath.
http://www.youtube.com/watch?v=ykikb_7Fxx4&feature=relatedI prefer to work with PVC as shown in the video. It's easy to cut and it's cheap. ACE will sell the parts separately or in a bag with all you need.
I suppose you COULD replace only the nut and the "compression gasket" that fastens the tail piece to the drain basket assembly but, for my money, you could spend 5? 10? bucks for the drain pipe kit and 12 bucks for the basket assembly and replace it all. Just mirror what you have now.
I like that tip in the third video of applying a little pipe dope to the compression fittings. Technically you shouldn't HAVE to do that on compression fittings but it probably save a lot of "fussing" with the connections. I'll have to try that.