Well, the principles are kind of complicated. There is an article about it in the startegy section. Also the ICM doesn't really give you the answer to what to push and what not to push. It just gives your stack certain value in $ based on how many chips you have and what the payout structure of the tourney is.
What the ICM trainer actually teaches you is the Nash equilibrium I believe. If you are pushing according to this your opponent cannot gain any chips from you in the long run. The best he can do is breakeven if he also uses the equilibrium. This is kind of complicated topic so you should visit some coachings and ask questions there where more experienced players can explain this.
When training ICM there are a couple of things you should watch out for. First is your position. You can push more hands from late position than from early position, of course.
Then your stack size in BB. The ranges are tighter with over 10 BB, get looser with around 10BB and get very loose with 5 or less BB.
Then the stacksizes of you opponents. You can push a bit looser into opponets who have fewer chips than you do because when they call you and lose they bust so they should call you less often and you can gain chips by picking up the blinds.
Then there is the bubble situation when only 4 players are left. That's when the stacks become very important. You can only very rarely call a push from someone who has more chips than you do, unless you are the shortstack.
When there are 3 players left the mechanics of the play change again.
I wouldn't really use ICM in the heads up if I were you so there's no need to practice it really when you are just beginning to play SNGs, IMO. So you can just set the ICM trainer to 3-6(or7) players and pracitce....
Anyway, sorry for the long post but you will have to read and practice a lot anyway if you want to master the ICM..
Have fun learning and good luck at the tables,
Lubor
P.S. You can play using just the charts but you won't probably win much and you will have to learn the ICM sooner or later anyway so sooner is better IMO..
P.P.S. The starting hands charts for the early and middle stage of a SNG are pretty good so you should stick to those. It's just the charts for push or fold that I don't like so much.
P.P.P.S. ♦ Watch videos and visit coachings. Those are great learning tools.