Fitting a sink waste involves installing a new p-trap. Plastic drains are easier to fit and last longer, but chrome provides a more finished look for exposed applications. Purchase the new trap and tailpiece along with the fittings to connect them at a hardware store. Use a saw to cut the pipe to length and water-pump pliers to tighten the fittings.
Install the trap arm
Install a slip-joint nut over the pipe facing down. Install a second nut facing up. Add the slip joint washer and insert the arm into the pipe opening in the wall. Check to ensure there is a minimum of 1 inch of the arm inside the wall joint. If the arm is too long, trim it to fit with the saw. Tighten the nut at the wall so it's snug but still allows you to make adjustments.
Attach the trap
Ensure the tailpiece from the sink is the proper length, cutting with a saw if necessary. Place a third nut over the sink tailpiece and add a slip-joint washer. Attach the trap to the tailpiece using the two nuts. Adjust the arm and trap as needed to ensure a proper fit.
Tighten the nuts
Once the trap is in position, hand-tighten the nuts. Use the pliers to tighten the joints more. Avoid over-tightening the nuts. Check for leaks.