For a simple join:
SELECT a.*, b.*
FROM tblAlpha a, tblBeta b
WHERE (a.keyfield = b.foreignkey);
It's often smarter to do an outer join, especially if you need rows in tblAlpha to show up in your resultset even if there is no matching record in tblBeta:
SELECT a.*, b.*
FROM tblAlpha a LEFT OUTER JOIN tblBeta b ON a.keyfield = b.foreignkey;
If you want to get into the nuts and bolts of it, the MySQL doc is found at:
http://www.mysql.com/doc/en/JOIN.html