Early game: To avoid getting ganked by the opposing team jungler, I would play safe until you reach level 6 then when you open your ult, block off the junglers path for ganking with your shrooms. If the jgl does happen to come, make sure you keep your laner at low health so when the jungler hits your shrooms and still comes for a gank, kite your laner because the jgl is already slowed and SHOULD be lowered to half health with your shrooms by the time they reach you. When you kill your laner/if they back off, go for the jgler and you should be able to have an easy kill. Try to avoid tanky junglers (Gregas, Tank jax, etc...)
(For opening abillities go to abilities tab.) Shrooms are very effective on squishy champions or even late game it can do as much damage to tanks. Keep your farm steady in lane, just make sure you don't be a nasus :).
Extra Note- if your confident in not dying with teemo, take ignite instead of teleport because early game teemo with ignite can be VERY useful.

Mid Game: The reason you rush Liandry's Torment is because you can do MASSIVE damage with teemo if you take the item. And the more you kill your laner, the more quicker you can take down the first turret in the top lane. As soon as you take the tower, clear the minion wave and rush a mid gank to help take the turret there. Once you take turret/your top laner comes mid, go back top and block the path of other enemies coming with shrooms. Farm until a team fight accumulates then go wherever it is happening.

Late Game: When split pushing in lane, make sure your safe (enemy top laner dead / in mid lane team fighting) take a tower and depending on how good your team is fighting mid, go mid or not. In late game team fights, using teemos ult to its best ability can be your easiest way at killing people/making them back off. Place your shrooms to either clear the minion wave or to deal insane damage to the other team. Prioritize at placing them just inside the mid lane so when the enemy tries to roam they get hit.
Tip: Always keep shrooms near you to escape/kill players.

Building Ludens Echo before Rabadons Deathcap can be very useful mid game and can do massive damage if your looking to delete other players (assassins, adc's). I would suggest in late game keeping shrooms in as many parts in the map as possible so you can get vision on any player who steps on them and you can track them down easily :).

You can take other masteries for teemo but I would NOT recommend these masteries in a ranked game unless your feeling risky.

In my opinion this is the best build for teemo (scroll up to see build) if your want full AP. You can build other situational items like - Rummans Hurricane, Hextech gunblade, or Zhonya's Hourglass

As I have already mentioned, you want to place your ult in as many places possible to protect and attack. If your against a top laner that relies on their aa then if you engage you want to q as soon as possible. If your trying to poke your opposing laner then I would auto attack twice then use your q for best results.

Building Rummans Hurricane can help keep your farm up a lot :)