That error generally means you don't have MySQL running. Generically:
Should start the daemon, however, you probably have an init script of some sort, maybe a:
Will do the trick, depends on how your distro sets that up.
As for a "GUI" I'd probably guess you will want to use PHPMyAdmin which runs through the browser for your MySQL admin needs, you can also look at webmin, but I think generally people use PHPMyAdmin a bit more often.