Super Smash Brothers has a relatively limited set of moves, and there are no special "combos" like in other fighting games, where you press a sequence of buttons to perform a particular move. (haduken, for example).
On my my friends favourite games back in the day was Killer Instinct Gold on the N64. I had no idea what I was doing. I have the SNES game now... still have no idea what I'm doing. I'd have to look it up to figure out each characters particular moves. The difference between Smash and other fighting games is that you aren't rewarded as much for memorization. The best you can go for is to chain together series of movies based on how they work, but that is far more dynamic than arbitrary button and directional inputs causing you to throw a fireball. For example, here is the reference sheet for each character in Street Fighter II:
http://streetfighter.wikia.com/wiki/List_of_moves_in_Street_Fighter_II
Notice how each character has different sequences, so that if you switch characters now the moves you are familiar with don't work. So for those games, players tend to specialize more.
With Smash brothers, these "combinations" are more limited. you have two buttons and you can only combine them with the control stick. You can either press it without using the control stick, tilt the control stick, or tap the control stick while pressing the button. Each combination has a different move for each character, however the combinations are all the same; for any character, Up+Special will ALWAYS be their recovery move, for example. They all dodge and roll the same, etc. the differences are more in the character's style. Mario's recovery is the Super Jump Punch, for example; whereas Pikachu's Recovery is Agility. Each one works subtly differently, so practicing with a character can help you learn that characters particular traits, but the basics apply to all characters and you don't need to reference any website like the one I linked above to find all of a characters moves, because the actual inputs are the same across the roster.