Well, it's not too hard.
There are a few concepts to understand in 2D fighters (3D is a whole different ballgame, unless it's a pseudo-3D fighter ie the SFEX series).
The first and foremost to learn and master is how hits affect your opponent. I'm not talking about damage, but more about what happens then your hits land, what condition your opponent was in, etc. This will help you master the flow of the game, and how you can actually make up your own combos as you go along, which is part of the fun of fighting games.
Usually, what happens is one of the two following situations:
1- Your hit lands or
2- Your hit is blocked.
If your hit lands, your opponent gets into a state called hitstun. Hitstun is basically a small window where the character is "stunned" by the hit and is unable to act. This is the basis of combos: chaining hits together through hitstun. Most games allow for cancelling, which is the act of cancelling your attack's animation by another attack to exploit the hitstun state. In most KOF games, for example, you can cancel a normal standing strong attack (B or D button) by performing a command normal attack (ie usually forward + weak punch or kick). This forms a basic 2-hit combo. You can also usually cancel the strong attack by a special attack. You can also sometimes (this really depends on your character) cancel that same original strong attack with a super move. This is how you usually land your supers (Desperation Move or DM and Super Desperation Move, SDM). Other situations are possible, but usually shooting supers out of the blue is generally a bad idea, unless you know for certain that it will actually hit.
If your hit is blocked, well, you just have to handle it. In most fighting engines you can still do your combos on blocking opponents, although you should practice stopping before launching off any special or super move if your opponent is blocking your combo, as they usually have rather large windows at the end that leave you completely vulnerable.
What I would recommend is hitting up your favorite game's practice mode, pick a SINGLE character you would like to learn (most people around here can help you out with which character might be the easiest to start with), learn the timing of his/her attacks, practice your moves/supers and find ways to combo them. It's really important to pick a character and stick with it; you can then learn all the basics. When you'll try another character after mastering the basics you can then easily switch characters, learn their moves and be able to play them with relative ease.
It's not that hard, and you should get the hang of it relatively quickly. Remember that those long motion supers should take you less than a second to perform, so learn to do them quickly.