In the current META these are the following roles: Solo Top Lane, AP Mid, AD Carry Ranged, Support and Jungler
By now, you should have your favorite champion or roles. If you do not have any yet, you better pick one and learn the skills.
The following details are a summary from video that I watched over on the internet, mostly are from LAN competition or Go4LoL, where team already arrange their team composition previously. I can’t really comment on Solo/Duo Ranked Team.
Solo Top Lane
Usually the champion pick will be a tank bruiser(Shen, Gangplank, Riven, etc) or an assassin type(Irelia, Talon, Akali, etc). Some team do run double AP lane (Kennen, Rumble, Vladimir, etc) where they build double Will of the Ancients for their AP champions. Most of the time top lane will be left alone and farm all day. Couple of players that you can watch their stream/youtube are TSM Dyrus, CLG HotshotGG, CLG.eu Wickd, Dignitas Voyboy, etc. After watching 4Deman youtube shoutcast, I found this spreadsheet from wickd about top lane match up click here.
If you search around the internet or youtube, you will find there’s a lot of option for jungler even some people believe all champions can be a jungler. I believe the basic requirements are ability to clear jungler very quick or strong Crowd Control skills (slow or stun). For safe jungle example, I would recommend TSM TheOddOne guides. If you are interested in aggressive jungler search for IEM on MoscowFive Diamond match or exGBT/MYM Makata(not sure about this one since he use a troll name) video on youtube.
Solo AP Mid Lane
As the title say most of the time this lane belong to Ability Power champion which will carry the game(Karthus, Mordekaiser, etc) or roam around to gank(Le Blanc, Sion, etc). If you are able to farm and get kills when it come to late game you will become a scary monster or unkillable due to your sustain/CC. You do need to be aggressive on this lane and work together with your jungler to get early kills. Note some champions are quite fragile pre level 6 (Swain, Kassadin, etc) and there are 2 non ap champions which commonly play in middle(Talon and Caitlyn). Dignitas Scarra, TSM Reginald, MoscowFive Alex are a good example for super aggressive AP mid.
AD Carry Bot Lane
On a Ranked 5 team or Competition, this role will be filled by AD carry ranged. On Solo/Duo Queue, you never know what the other team gonna do until you see them in lane. As an AD carry you need to farm and deny creeps from enemy AD carry, if you can work together with your support you may get some kills. Your main objective is to outfarm the enemy AD carry, depending on how’s the laning phase go you can go straight to major items such as Infinity Edge or Blood Thirstier. Most common picks are Vayne, Graves, Ashe, Corki and Sivir(unsure about Sivir since the last nerf), some EU teams has pick up Kennen as their AD Carry. Pro players to follow are TSM Chaox, MoscowFive Genja, exGBT/MYM Makala(not sure about this one since he use a troll name)
Support Bot Lane
As support you do need to support your AD carry to farm and get kills whenever possible, in addition to that you also need to ward around to give better map awareness. For this position most of people will expect the standard support champions. The most popular picks are Janna, Sona, Soraka, Taric, Alistar, Lulu and Nunu. However, I have seen couple of other more offensive champion being played as a support, i.e. Nidalee, Maokai, Oriana, etc. Same as jungler it’s if a support has heal or CC ability.To be honest in Solo queue support is underrated, not a lot of players want to pick up this roles. Due to the nature of the gameplay where you need to sit back and not killing minion. For more in depth guide I suggest for you to read TSM Xspecial overview on support role
Note: this is only a basic summary of each roles, there are different possible way or method in playing or what best for each roles. If you want to get better I suggest for you to watch LoL video on youtube(links can be found on my video page on the top) or read some guides that available over on solomid.net or mobafire.