My drainage pipe is leaking when the water is draining from my sink. The attachment pipe is directly attached to the drainage hole of my sink. It seems the "connector" from sink hole to pipe is corroded. How do I change it/replace it.

If you have chrome piping that's leaking and correded I'd recommend that you replace all that you can reach with a PVC drain kit. Most home stores sell a kit that has a drain pipe, extension, trap and horizontal pipe. The PVC can all be done without tools but you may have to cut the extension tube to fix your sink.

Ballengerb1 is right, you can get the PVC kit from Home depot/lows it is very cheap no special tools required the only thing you may need a cutting saw to cut the extension tube to the size as Ballenger says, PVC will never get corroded.