Use the grant permissions command.
If your database name is "newdb" and user is "newuser" the command to grant all privileges on all the tables contained within would be:
mysql> CREATE USER 'newuser'@'localhost' IDENTIFIED BY 'password';
#if user needs to grant access from the remote machine
mysql> CREATE USER 'newuser'@'8.8.8.8' IDENTIFIED BY 'password';
mysql> GRANT ALL PRIVILEGES ON newdb.* TO 'newuser'@'localhost';
#if selective permissions need to grant
mysql> GRANT SELECT, INSERT, DELETE ON newdb.* TO newuser@'localhost';
mysql> SHOW GRANTS FOR 'newuser'@'localhost';
mysql> FLUSH PRIVILEGES;
mysql> DROP USER 'newuser'@'localhost';