Where to find skills

First step, try to focus on dying less.

Second step, learn to read situations. This connects heavily with step one.

The rest will come.

So at the leftish side bottom of your screen, you'll see your champ picture. Immediately to the right of that are 1 small square and 4 big squares. Note: these squares will be in between your champ portrait and your summoner spell icons. These squares have cool pictures in them, and clicking on them will activate the skill that is associated with the picture. However, only the 4 big squares are clickable, the small square contains information about your passive and cannot be activated by clicking on it.