For hashing you have several supported algorithms in System.Security.Cryptography, for your usecase you probably want to choose an SHA based hash or something similar.
Regarding the comparison: You don't compare the DB value and the one the user gave to you. You use the same encryption/hashing function that you used to store the password in the DB in the first place, this time with the user input. If the result is equal to the hash in the DB the password was (probably) correct.
The intention is that no one that has access to the DB can retrieve the passwords in clear text and not even your program needs to know about it (only the part that accepts the user input will have it for a short time).
Links (maybe even duplicates):
