How do I use an old desk as a vanity?

Lisa, if you mean with plumbing for a sink, you need to make the back accessable

for the pipes, choose your sink & faucet and may have to cut out a drawer to allow room for the pipes.

There are many tutorials on this site for that.

Make sure to waterproof the wood vanity for moisture and water spills.

Water swells wood.

If you mean a simple Vanity for makeup and grooming, then what you need is a large mirror hung on the wall behind the former Desk. A low shelf or boxes can be placed for storing toiletries along the back. Using paint you can decorated t all as you choose.