The Support Role --
I've divided the Support Champs into A, B, and C groups, based on three factors. First, can they sustain their carry in lane without the need for Heal? Second, how easy is it to harass the enemy carry and keep them off their farm? And third, how likely, in blind pick, are you to get hard countered by the enemy teams' composition?
A Champion in Group A is always a safe pick, and I strongly recommend becoming good with at least one of them to start. As you begin to play draft games and ranked matches, you will need to add a few more Champions to your repertoire, and at that point, I recommend picking up a few of the hard counters to make your options as flexible as possible. Namely, you'll have your main Champion, if the opposing team doesn't pick a Champion which counters you, you can just go with that, and you'll have a stable of counterpicks to work with if they do find someone randomly that hoses your strategy or playstyle.
Support Group A -- Alistar, Blitzcrank, Janna, Leona, Lulu, Nunu, Sona, Soraka, Taric.
Support Group B -- Galio, Gangplank, Karma, Kayle, Lux, Teemo, Zilean.
Support Group C -- Morgana, Nidalee, Shen, Yorick.
Also, with this list, keep in mind that some of the Champions appear in a lower tier than you might expect, and your mileage may vary. In general, Champions listed in Group C play better as carries, junglers, or solo lanes, and using them as support is often something you will only see if they have a strong laning phase against a particular Champion on the other team. Truthfully, any Champion can play support, if forced to, which is why you'll notice this list is shorter than the others. But sticking with the characters you see listed above will definitely improve the quality of your support play, and teach you how to play support most effectively.
Support Objectives --
1) Harass and Sustain (Early Game) -- As with any solo lane, farming is the carry's most important objective. When you play support, your job is to keep the carry alive and farming. In order to do so, you need to keep the opposing Champions away from them, and, ideally, keep them underfarmed.
The most effective way a support can help win bot lane is by literally standing between the opposing Champions and the minions they are trying to farm. In order to do this safely, the support must buy wards to watch for enemy ganks, and also to help protect the ADC.
I recommend placing a ward in your tri-bush and near the dragon pit, if Blue, and slightly below the dragon pit if Purple. The following image is a great guide to placing wards all over the map. It comes from the League of Legends forums, and should be a huge help when starting out in the game.
2) Counter-jungle and Ward Clearing (Mid Game) -- As the lanes get pushed, team fights and map objectives become more important. Depending on which support champion you've chosen, you may not have a whole lot to do during encounters with the enemy team. As a way to offset the offensive limitations of a support character, you can pick up Boots of Mobility and Oracle's Elixirs, to go along with a collection of wards, and scout the map, clearing away enemy wards and setting up your own to greatly increase your team's map awareness.
While you are doing this, it is a perfect time to ward the neutral minion camps in the opposing jungle and steal experience and gold whenever you find them unguarded. Doing so sets back the enemy team, and can grant bonus buffs to your allies (if your team has both Red and Blue buffs, they will have a distinct advantage in roaming team fights).
3) Help Win the Team Fight (Late Game) -- As the support, depending on the champion you've selected, you will play different roles in a team fight. The two primary designations for supports are Tanks and Healers.
Tanks -- Alistar, Blitzcrank, Nunu, Gangplank, and Shen can all have massive health and armor totals near the end of the game and playing as these supports often mean wading into the middle of the fight and trying to attract as much attention as possible. In the perfect situation, the enemy team will actually start focusing you, giving your AP and AD Carries plenty of time to kill their squishy opposites. All five of these Champions have AoE CC that can further turn the tide of battle to your side.
Healers -- Sona, Soraka, Taric, Nidalee, and a few others all have abilities that restore lost health to their allies. In a team fight, they will alternate between casting targeted or AoE CC spells at the opposing team and healing their teammates.
Other support champions have abilities that Taunt, Charm, or deal massive AoE damage. Some have buff abilities that raise attack damage or attack speed or help increase armor or magic resistance.
In general, if you have a spell that adds a buff, using it on your carries is going to be the correct play, because they are your main source of damage. Likewise, if you have a debuff ability (lowering attack speed or armor, for example) then you want to target the enemy carries, in order to take them out of the fight faster.
Support is a challenging and engaging role to play on a League of Legends team, and this guide should help solidify your understanding of how to get started. One reason I love playing support is because it is such a different way to experience the game. You have unusually objectives and unique gameplay situations, and when you do your job right, the whole team looks better. Also, you get to die a lot more and not feel as bad about it. (Every time the support dies, it means that a carry lived, and if the other team doesn't realize it fast enough, the game is going to be over rather quickly.)
If you have any further questions or would like to see this topic revisited in an Advanced Guide sooner rather than later, e-mail firstname.lastname@example.org, and tell me why or just head to the comments. Odds are, you can even be first!
Until next time, may all your ultimates end in kills and all your games with "Victory."