First loosen the nuts on the drain trap(the curved part)from the bottom of the tailpiece. Then loosen the nut holding the tailpiece to the sink basket. Replace with appropriate diameter and length tailpiece(cut if necessary)making sure gaskets are in place. Hand tighten.
Replacing the drain on a kitchen sink is not tugh. the plumber's putty underneath the metal flange can dry out and crack. The rubber seal located on the underneath side of the sink either come loose. Just take anther pipe and fit and seal the edges with sealer.
The first thing you do is unscrew the old drain tail from the strainer, they you get the new drain tail piece and screw it back from were you took the old one from.