How do I play Annie support?

Take E at level 1. Sit on fountain and get your passive stacked up before heading into lane with passive ready and full mana. Hit level 2, take your Q, begin applying stuns to the enemy anytime they're in range. Dancing about in the bushes is a good way to do so. Bide your time until 6 while keeping your enemy laners feeling the heat, drop Tibbers and begin going ham. Your base damages are MORE than enough alongside an ADC's attacks.

Rod of Ages -> tank with a focus on MS and CDR for your build. Wardswardswards when possible. If you start getting super fed off kills and assists, grab that Mejai's, earlier the better. But I wouldn't suggest that until you're SOLID with her as a support and can make the best use out of it.

Your job as Annie support outside of the laning phase is basically to make sure you land Tibbers smack in the middle of the important teamfights and stun as many people as possible while giving yourself a good deal more durability than a bursty mage should ever have while running on your base damages slightly augmented by the RoA.

Runes and masteries are generally preference for this. 9/0/21 can give you a lot of utility with a slightly smaller focus on damage, while 21/0/9 can give you a bit more damage and at least some mana regen to get through the early game. I've seen some Annies run 21/9/0 or 9/21/0 if they were planning on being super aggressive and wading through minions to land Q stuns early. Runes you're probably gonna want magic pen reds, armor yellows, mr/lvl glyphs (scale better into late game) or possibly CDR (more spells = more stuns). Quints you're going to want AP or MS.

Generally you should get more MS on support annie if you are the initiator. I usually go spellthiefs into Mobis into sightstone. From there it can vary, distortion enchant if I need more flashes, change spellthiefs to talisman for an aoe MS buff, Rylais for a constant slow from tibbers, I've even seen righteous glory in LCS play just to make Annie tankier while giving the MS.

You can go more damage if your team already has an initiator/you need to carry dat scrub team full of feeders but without the farm and kills that mid Annie gets you can become underwhelming and just be a detriment to your team

Edit: grammar and future-tense is hard :P

When I seen my first support, I flipped out. It scared me a little

You don't build the same at all. Annie bot lane is not about damage...it's all about instant/flash engage. Generally go spell thief's blade...get your site stone, build mikaels if needed etc. Your job is to team fight engage for your team or ADC. Flash Tibber stunning multiple opponents is what you're all about. You're all about vision and stuns, you're not meant to be a damage combo champ like you are in mid lane.

AP. Wombo