Salt-and-hash the user's password as normal. When logging the user in, allow both the user's password (after salting/hashing), but also allow what the user literally entered to match too.
This allows the user to enter their secret password, but also allows them to enter the salted/hashed version of their password, which is what someone would read from the database.
Basically, make the salted/hashed password be also a "plain-text" password.
