A couple of methods.

The first is to copy 2 files, key3,db and signons.sqlite from the profile folder of the old computer t the profile folder of the new computer. For details of how to find the profile folder see the profiles article.

The second method is to install the Password Exporter add-on on both computers and use that to export/import the passwords.

If you copy key3.db and signons.sqlite then Firefox will automatically use the old Master Password because that master password is stored in key3.db as part of the encryption key.

See also http://kb.mozillazine.org/Password_Manager