Should you go solo top to farm, or go bot and constantly be on your toes because you will have to keep your lane buddy safe? If you go bot, you won't farm at all because your lane buddy has to farm up good to be effective, but on the other hand you won't get any money except from assists, which, depending on aggressiveness, may not occur often. So how should you play these support champs?
Each support champion plays a different role (e.g Teemo would play differently than Sona, Soraka would play differently than Fiddlesticks). If you're looking at a specific support, perhaps you should ask "How do you play Sona as support effectively?".
In general, if you're claiming the role of support your biggest responsibility is do cater to the whims of the range AD you will roll with bottom lane. Often times when I play support I'll ask the range AD which he/she would prefer (Some like having the auras and diversity Sona can provide, while some like the extra control Janna can offer, and others like the extra mana from Soraka).
Regardless of the support champion you end up with there are a few important jobs you have:
Playing support will take some getting used to, but they can be fun. Don't expect to be the highest level on your team, don't expect to have a full set of items quickly, don't expect to be rich. Unless your character can handle it, you shouldn't be near the front of team fights.
This is only some basic tips, and I'm sure I'm missing some, but it will get you going.
Here is a really excellent guide that covers almost all the aspects of supporting.
The guide covers:
What Makes a Good Support?
Set Up for Success: Runes & Masteries
The Usual Suspects
Items and You
Who to Watch and Why
Excerpts from the guide:
Early game: You want to be in the lane with your carry, and let them farm. Keep them alive, protect them and don't steal their farming. Help them harass but let them take the kills. You should be putting your skillpoints into the spells that bes aid your carry. For example, as Janna I always max the shield first for the protection and the AD bonus. You should be warding consitently during this begginging lane phase.
Mid game: You should still be warding and supporting your team, never wander alone and always keep your teammates safety in mind. Keep an eye on the map and call MIAs and start building some of your base items. You want to build survivability that will benefit not just you but your team. Aeigis, Frozen Heart and other aura items are great support items. Always be using your CV(which you should have) to scout the enemy positions. Keep an eye on your carry and go with them to perform ganks.
Late game: You should be focusing on being there for your team as a whole, whatever they need in those teamfights you deliver. If you find your carry is getting focused then make sure to use your interupts and shields to keep them alive, if the carry is ok then defend and heal the tank if he is taking a lot of damage. build your build around what you are needed for, sometimes if your team is very sustainable you can even afford to beef up some of your damage! (not likely). Continue to ward river, Baron, their jungle. Late game CV will make or break the game. Learn how to use your skills to get an advantage in those teamfights, support characters can be very disruptive and effective.
Random tips: Gold generating items such as heart of gold and philosophers stone are great on support characters. You will be surviving on assists and have to buy a lot of wards. It wouldn't hurt to put some points into the gold generating mastery. Remember when building to keep your team in mind. Don't just build AP and think that will make your heals more effiecient thus making you a good carry. You also want to have good unique items with good auras.
Basically a support player needs to forsee tragedy before it happens. A well placed Wish from Soraka can make or break a teamfight as can a well place monsoon?(jannas ult). By giving your carry or tank that extra sustainability with that kill they thought they scored could break the whole team. A monsoon can save teammates or place the enemy carry in a bad place.
Support should always and always remain bot with the AD. You want to keep the AD safe and let him farm well to carry late game.
You are a support, meaning you dont need gold or anything. Just get assist.
Get Heart of gold and philostone, that is your main source of income and assist. Support should not farm over AD.
Support means you are supporting your partner and keep him alive. You play support by constantly warding and constantly try to save your AD carry or other champ in team fights. There are many different support champ but your main role is to keep your AD carry safe and let him farm.
Support champions often work best when paired with another champion. Their abilities typically focus on buffing allies and debuffing enemies. With the current meta, it's very common to see a ranged ad carry bottom with a support (though many other options exist).
In order to maximize the effectiveness of a support, it's important to look for skills that synergize with your lane partner. Taric and Vayne have a great stun combo, Graves and Soraka have amazing poke/sustain, and Alistar + Blitzcran have undeniable crowd control.
It's very typical for a support to give most (or even all) of the creep score to their partner, because the carry is very item-dependent. In this situation, it's best for a support to buy GP/10 items like a philosopher's stone, heart of gold, etc.
Finally, a support's most important job is map awareness. Via wards, clairvoyance, and roaming, it's important for a support to always be aware of what's happening on the map. This compounds with supports that have global ults, like Shen or Soraka.