How can I hash a password in Java?

I need to hash passwords for storage in a database. How can I do this in Java?

I was hoping to take the plain text password, add a random salt, then store the salt and the hashed password in the database.

Then when a user wanted to log in, I could take their submitted password, add the random salt from their account information, hash it and see if it equates to the stored hash password with their account information.