APs Teemo Build:

dagger(400g) + 2 health pots(35x2)
recall: dagger(400g) or stinger(1250g)
recall: into stringer(1250g) or after stinger: Fiendish Codex(820g) §Amplifying Tome(435g)
§Fearie Charm(180g)

recall: Nashor's Tooths (2500g total) + 2 wards / rest value for pots.
Since the new patch, nashor's tooth has obtained the Malady effect, scaling over AP.
So teemo gets an entire refresh for any ranked play.

Ruby Crystal (475(if being pushed)) or Amplifying Tome(435g)
recall: build into Haunting Guise(1485(+575))
recall: Amplifying Tome(435(+980)) into Liandry's Torment + wards and pots.

if your losing the lane: Instead of Liandry's, get catalyst after Haunting Guise.

Long Sword(400g) + (Vampiric Scepter(400)=800)
into: Bilgewater Cutlass(1400g)

recall: daggers x2(400+400(800))
recall: Blade of the Ruined King(3200g(+1000)) + wards and pots.

If your building your "e" Skill with teemo, you might wanna get this:

Hunter's Machete + Fearie Charm + Rejuvenation Bead + 40g: Spirit Stone(700g)
recall: Long sword x2(400+400(800)) + 500g into "Spirit of the Elder Lizard"

Now in this stage of the game, you'll be very strong with autoattacks.
You basicly have your poison dot, ignite, mask burn + spirit's burn.
If you ask for a red buff aswell in this case, you will probably need 6 to 12 hits to kill a top laner, depending how tanky they are.

Now you might think, why do I still not have any boots.
Well, somewhere in the build, you can decide for yourself when you think boots is viable.
You pretty much have a bunch of choices:

If your dominating your lane, and are gank free, you can start getting boots of mobility(with furor) to start roaming after you downed 1 or 2 turrets.

In case the top lane, is easy but too tanky to kill, you might wanna go for Magic Pen boots(with furor).

If you don't level your W at all, and just leave it at level 1, you might wanna go for AS boots after the nashors tooth for the extra damage from the passives.

If your getting pushed and your losing, you should probably get ninja tabi or Magic Resi boots depending on what your enemy jungler and laner are playing.

At this point you wanna go for some lifesteal extra (ruined king has some) or flat attackspeed.
ok, so since the boots weren't really a necessarry item, you have the posibility, to increase your attack speed, attack damage + movement speed and tenacity, with the item Zephyr.

Zephyr stats aren't for AP teemo, but it's still usable because of the MANY stats it gives.

+25 Attack damage
+50% attack speed
+10% movement speed
+10% cooldown reduction
+tenacity.

The item is quite expensive so it will take a while to obtain. (2850g)
"just a note:" Zephyr is also a great choice for any AD carry's in lategame, when boots become optional.

Your sixth item, is quite optional to the situation of the game, you might wanna go with more damage (deathcap) or instead you could go more tanky aswell, depending on the score and team setup.

Here is some information for basic lane pressure and survival.

Just try to keep the river warded underneath the brush until level 6.
Once you can place your shrooms, the placement will be crucial.

If you wanna be playing VERY aggressive the entire game, you want to be placing the shrooms on key locations, like the enemy top brush, the river wall corners, and the tribrush.

Once you have it all shroomed up, you can still try to place 1 or 2 wards every 5 minutes, just to be sure, but the main thing that is important is, is that you can keep harrasing if you have it shroomed up, because once it's shroomed you can just do whatever you want. If the top laner decides to push back, you can still just move back through ur shrooms, and go invisible with your passive. Or on any ganks, your shrooms provide you with time to go into stealth.

Just in case the champions in their team are champions like Zac, nocturne etc.
You should ward your own brush aswell, since they will be able to ult or jump on you from your side of the jungle.

Ok this is what you want to do, if you want to make a kill on the lane.

Make sure that all the creep is dead, and the enemy is zoned out.
Then you use your passive to just go into stealth on the lane, let the lane get pushed, until the enemy champion is close to over the middle of the top lane.

Once he's on his position, try to place 1 or 2 shrooms on the lane, and you open fire with autoattacks.

Do not use blind or Ruined king yet, use it once he attacks you.
If you get attacked by the champion, blind him and slow him with your items (ruined king for slow), and start kiting with your W ability, move hit move hit move hit move hit etc.

In case he try's to run away instead, use your ruined king to take advantage of that, and start chasing him with your W.

The possible 1 or 2 shrooms are there either to slow him, or to stop the creep from hurting you badly.