you dont really have to try every champ, all you really need to do is see them played or look at their kit and decide whether that looks interesting to you and play it either when its on free week or when you get it.
and most roles aren't that complicated, i think the only real complicated role is jungle where you have to worry about smite buffs dragon baron ganking and scuttle crabs, etc.
for example lets say you saw lissandra played during free week(just an example) and you thought that looked fun so you looked at the kit lissandra has after the game and decided you wanted to play that you try her out in her normal positions mid and sometimes top in this case and if you dont like her look at other champs and/or roles until you find one you like or interests you. when i first started playing i personally loved the way veigar looked and played so i tried him out and liked him and hes basically one of the champs i used to learn mid, i also did a lot of volibear top and udyr jungle.
generally you learn in this game through reading(kits items guides etc) and watching others but mostly by just playing until you find something you like. and generally you can fit most champs into several different categories:pure AP, AP Poke, AP tanky, AP Utility, Tank, Bruiser, Juggernaut, fighter(personally i think bruiser and fighter are different fighter is more damage where bruiser is more tank imo), marksman, mellee adc's, AD casters, Assassins of either AP or AD variety, etc. so if you like playing one champion you may enjoy playing other champions that are similar
if you want more details on each role position or whatever i can give you more on each one