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