As mysql administrator, in the MySQL shell:
grant select,update,insert,delete
on DATABASENAME.*
to USERNAME@localhost
identified by 'PASSWORD';
Exchange DATABASENAME, USERNAME and PASSWORD with the relevant values.
Note that this works immediately; you do not have to re-load the MySQL grant tables if you do it this way. Actually, I generally recommend against Jay's suggestion. The GRANT syntax is easier and closer to what is normally the procedure on other database systems.