How can a random salt for a hash function work in practice?
Usually, when the user registers, you will generate a random value to become the salt. Then, in the user database, you store the user's name, salt, and hash generated using the password and salt (and whatever else is relevant for a user table).

Note that doing it this way allows each user to have a unique salt. Each user having a unique salt greatly increases attack difficulty. An attacker is forced to do a brute-force attack per user instead of precomputing per-password-scheme rainbow tables (no salts) or a per-database rainbow table (a system-wide salt). It is still your responsibility to make sure the brute force attack is actually slow enough to be costly to an attacker in these days of massively parallel GPU hash implementations.

Ideally, an attacker would not even be able to see the salt on the database, but it does not have to be private if worse comes to worse.