A common fault with most microwave ovens is one of the HT leads coming loose from the magnetron.
This can be fixed by soldering the leads to the magnetron terminals.
If your microwave is not heating then the magnetron may be dead, if you hear a click then buzzing noise when you switch the microwave on then it is more than likely the magnetron that's at fault.
If you don't hear the click and buzzing noise chances are that the transformer has gone in which case it would be more economical to purchase a new microwave.
PLEASE NOTE: microwave ovens store and discharge high voltages and should only be repaired by competent persons.
Alex Silverblade
February 2012