Controls are hot-keyed to keys 1-5.
You put the gems in the tower and they do damage to enemies. You can hover the mouse over the tower to read the description of what the gem does. Press the button to combine gems and drag a gem using the mouse over a gem in the inventory to combine them. The moats are great at slowing enemies down and towers are needed to put more gems in them.
As you level up invest all your skills in the powers for more mana. You can reset which powers your skills are in at any time. Once you are able to get to the first epic wave, you will need to go back and get better scores on the previous levels to level up to 19 and get all the mana powers.
The next big upgrades are for the buildings and the medium gems (high is the best). This is important because you will want to build towers in sets of (3,6,9) to get the corresponding bonus points at the end of the round. Also now you will be able to use the ctrl button when clicking on the build gems button at the end of the round to create lots of gems. Do the same for the combine button. Then throw all gems at the monsters during the final few rounds to get the bonus points for gem bombs thrown.
You get more points/mana by killing monsters as soon as they appear, so the best strategy near the mid/end of the game is just to stack the front where the monsters come out with towers and moats and put your best gems there.
For the final boss keep using the mana button for higher max mana and more mana, like a madman. Get it to around 40k. This will force the final boss to run multiple laps (he takes around 7,500 to banish). All you will need to do is have 3 level 5-6 purple gems get his armor down and kind of rotate them around the map in order to kill him