I think playing AP teemo is a little more difficult than ad/as teemo as it is completely based on mushroom placement and your ability to deal damage without taking any yourself. So if this is your first or second time playing teemo, I'd suggest using an ad/as build first and get used to the mechanics before trying AP.
Magic pen marks for obvious reasons, mp5 seals, and AP quints cause I feel the health from roa is enough, and the magic pen from boots/marks/masteries is enough. I prefer focus glyphs to celerity because it only ends up being a 2.3% difference and it takes a lot longer to stack up. Obviously going with celerity is fine as well, or even flat health quints/seals for an early zhonya's, just up to you. These runes/items/masteries get you to 30% passive cdr, and mejai's puts you at 45% (over cap) if you stack it up.
Teleport because you can port to shrooms which makes it great for putting shrooms behind your enemy right before a team fight, and Flash for great getaways or early game bursts.
Start with Meki Pendant and health potions for early harassing and so you don't have to go heal too soon. I get mejai's first cause depending on how often you get ganked mid or your team ganks mid, it can start stacking with assists pretty quickly. Then codex for the cooldown reduction before sorcerer's boots because your move quick+mastery should keep you quick enough with regular boots. I like to get roa because of the health/mana boost so you don't die instantly. Deathfire for big nukes since your ap should be pretty high around this time with mejai's. Zhonya's for a huge ap boost, and if the game ends up lasting this long carries will be hitting ridiculously hard and you'll probably be attacked pretty soon, so the 2 seconds of immunity will give your team time to scare them off. Finally a lich bane, if somehow the game lasts incredibly long this will give you everything you want, ap, move speed, and another big nuke.
My build focuses around having good cooldown reduction while still having enough ap for your shrooms to be effective. Plenty of items are interchangeable with others if you're looking for a specific stat more than another. For example getting an early zhonya's is great if you're not worried about health, or dropping the cdr runes and picking up a nashor's tooth instead of lich bane. This build is just my preference.
If the team is using wards, always buy 2 or 3 yourself and find them. However if oracle's elixir is involved you have a more serious problem. That person needs to be killed ASAP before he runs through the forests and kills all your shrooms.
Try to get mid as it allows you more xp so you can get shrooms faster. Once you get them you can choose to stay or swap with someone so you can shroom forests easier, up to you. Last hit mobs and once you get 2nd rank of Toxic Shot start spreading it to two or three creeps if you're dealing with someone that pushes creeps hard. If your enemy gets too close blind dart/auto attack for great harassing. Once you get your shrooms put them in the left and right bushes to avoid ganks, then the corners of the side lanes to maybe hit your mid target and avoid ganks from those spots as well.
Your mejai's should be up a few stacks now due to assists if not your own kills, and you should be holding on to the ogre buff as much as you can. Start shrooming the forests for vision of the enemy team, especially good gank spots. Just make sure your lane stays ok and you keep your ult on cooldown.
Make sure to use your deathfire/blinding dart on the enemy carry as soon as they initiate, and always make sure you're spamming shrooms in getaway spots(yours and theirs) and on the sides of the lane being pushed.
Keep your move quick on all the time but if it gets removed and you're worried about being focused very shortly, don't reapply it until you've flashed out of danger.
Always remember when shrooming forests that people tend to run towards bushes to escape, so put them there. Also people tend to cut corners so don't put your shroom at the center of an entrance.
Rod of Ages gives you enough breathing room on health to play a little aggressive, but the idea is to not be the kill target and keep dropping shrooms, so avoid damage.
You can score an early first blood if you're able to harass someone to very low health and they stay, just flash and blind dart/auto attack to unexpectedly finish them off.
I know they say AP teemo isn't as good as attack dmg/speed Teemo, but I think if you have a team that knows how to use your mushrooms to their advantage, and does, it ends up working out way better. Hope this helps.