Left controls

A - beats red goblins, green and blue goblins are immune.
S - beats green goblins, red and blue goblins are immune.
D - beats blue goblins, green and red goblins are immune.

right controls

L - beats red goblins, green and blue goblins are immune.
K - beats green goblins, red and blue goblins are immune.
J - beats blue goblins, green and red goblins are immune.

Noticing a pattern? That'd be because the inner keys block blues, mid keys block greens and outer keys block reds. So that can be handy if you want some info you may or may not use

You're going to want to kill these guys, not with an AK of course.

For an instance like this, LDJKA would be optimal, but you can just spam all the keys at once, but then your combo won't grow, with a combo you can get a nice high score.

Buying new mages requires gems, which you get by playing the game. They aren't easy to come buy to begin with, but become more common as you keep playing. Use them to purchase the mages. to do so, click on the gem count displayed below the mage when it's not grey anymore.

Buying upgrades will boost how much mana you get per game and increase the chance of getting a gem. It also improves the look of your tower too.

Yell at them to stop and spam the keys you use to defend. That is my simplest answer for that. Say 'allahu akbar' multiple times, then osama will appear and blow them all up (warning: does not work for non-isis members)

If not, go back and read the guide again until you get it.
Congrats on learning how to play by reading this guide instead of just learning it as you go. Now go and kill some goblins like a dank memester wizard.