Why Support LB?
The first player I heard of playing LeBlanc as a support was SK Telecom T1's PoohManDu. He plays it occasionally when his team comp is focused around stomping the lane phase, or when he wants to support carry/become a powerful late game assassin. He takes summoner teleport on it and uses this spell to make big plays, often as soon as it is off cd.
How to Play / Strength and Weaknesses
In lane: LeBlanc is very hard to beat in lane, with targeted stuns and counter burst being her biggest weaknesses. She does a ton of burst damage and can catch enemies with cc to set up easy kills for her carry. Once she has chains, she can look to teleport top or occasionally mid so set up kills or get herself fed.
Damage scaling: Her damage in the early game is immense. Her damage in mid game is still decent, thought not comparable to a mid LeBlanc. Her damage late game is equal to a mid LeBlanc, allowing you to 1 shot carries easily.
Utility: LeBlanc's cc is underrated. Her double silence poke/burst takes away the opportunity to counter play, as well as removing the ability for an enemy to jump to safety when being bursted. Her chains are VERY strong. Double chain locks enemies down for a very long time, allowing her and her allies to kite dangerous melee champs such as Nasus, Riven and Singed and take them down. Chasing people down with her mobility and then using a chain or two can set up kills for you team even when the enemy is miles away and thinks he is safe.
Mid game: With a dip in damage at this point, LeBlanc's mid game is focused on looking to set up team kills with cc burst combos. You cannot take on champs by yourself at this point so stick with a buddy until you are more fed. If you see a low health enemy however, often you get gap close and finish them easily with a combo. Don't feel stuck to your ADC, often roaming will result in kills that let you buy your first damage items and begin your support carry snowball. Because of this, I often tell my ADC to play champs who can safely wave clear/avoid dying when I roam. When roaming (as well as in lane), try not to take kills from the carries when possible. In the kill taking priority order, consider yourself below the carries, above the tanks and above the bruisers, unless the bruisers need the kills to get a lane edge.
Late game: At this point you are looking to catch squishies and one shot them. With DFG and Sweeping Lens look to camp brushes and make picks. Once you have made a pick, get your team to take objectives or start team fights. If team fights occur, whether you have made that pick or not, look to burst down whichever squishy is most fed.
Vision: You are a support carry but YOU STILL MUST WIN THE VISION WAR. Get your stone early. The health on it will actually help in lane too so don't feel you need to rush damage in order to fight. Keep control of key areas with your stone throughout the entire game. Switch out to Sweeping Lens when you feel it is time, often this is when you get your stone or shortly after. Do not upgrade to red stone until you have your damage items completed.
Choose between Ancient Coin and Spellthief's Edge, depending on whether you not you can regularly and safely harass. Upgrade to version 2 ASAP.
Start ward trinket. Swap for sweeper when you feel you need it.
Build sight stone early and ward properly because this is your job... Also extra vision lets you juke more safely + make great picks. Sit on blue stone until you swap your trinket out for red trinket, then upgrade.
After these support items, start building damage. This was not viable in season 3, however now you can get enough gold to full burst carries in the late game. You can choose to finish your gold item if you feel the active would benefit your team comp, or just leave it at stage 2 and get more damage items sooner.
The order of your damage items is situational. I like to go Deathcap > Void Staff > DFG > Zhonya's, however feel free to get DFG or Zhonya's earlier if you feel they better suit the the game or your playstyle.
Max Q first for best damage output and harass.
Max W second for the reduced cooldown, and the fact that Q > W combo is so easy to land. E max second is viable as the single combo damage is actually slightly greater, however the utility on E doesn't scale and the reduced cooldown on W is very important.
Max E last. You can put a few points in E instead of W if you are having mana problems, however mana is not usually an issue.
Points in Mimic 6, 11, 16.
Full AP masteries give you an immense early and late game. Utility masteries would let you reach late game faster among other things, however you would not have the damage needed to really punish squishies.
You can choose to go 21/9/0 or 21/5/4. Both are viable. The trade off is being a bit more tanky vs. a quicker back to help you escape sticky situations after you have managed to juke your way to temporary safety, as well as some handy mana regen.
There are no real alternatives here. You want whatever will win the early game the hardest.
Quints: Flat AP for big early burst.
Marks: MPen for big early burst.
Seals: Flat armor for early engage/poke survivability.
Glyphs: Flat AP for big early burst.