Hi everyone, I am Soloeco, I am playing on EUW and I am actually Silver but playing Teemo since season 2. First I played Teemo with as much AP as possible to kill the ADC or Mid-Laner very fast. But now there are many tanks in the actual meta so we need much damage over time to kill a champion like Mundo or Shyvana in lane. Otherwise they just would build magic resist and your 'fast-kill' is not possible anymore against the enemy laner.

The general summoner spell is Flash, because Teemo can't jump over a wall like Lee Sin to escape.
The second spell is in my opinion situational. I take Teleport when the enemy is in the position to poke me and/or underpress me with much damage. So I can go back more often if needed without loosing too much minions and experience. The other choice is Ignite if I know I will simply poke my enemy and can play more offensive.

Nashor's Tooth is an essential core item for attack speed and its passive for bonus dmg per attack scaling with you AP.
Runaan's Hurricane is important for a fast push (waveclear) and in a teamfight your posion effects on up to 3 enemys at the same time.
Guinsoo's Rageblade gives you the needed AP and AD for good damage and the passive is also nice in teamfight to hit more than just one enemy.
Liandry's Torment is pretty helpful to not getting oneshot by an assasin or to easier kill a tanky champion.
The last item of your build is situational.

Example 1: If your enemy team having Zed and he is fed so you can build Zhonya's Hourglass to break of the damage by his Ultimate. Or against Caitlyn Ultimate. Also the bonus armor helps well against a team with much AD.

Example 2: If your team is ahead and you chase them down you can build Frozen Mallet to slow someone. So your team can better kill him.

Example 3: If you need extra damage against squishy enemy team build Luden's Echo with AP and movement speed or Rabadon's Deathcap.

Example 4: If they have many tanks with much magic resist you can build Void Staff for magic penetration and extra AP.

Example 5: If it is very importat to stay alive your best choice is Guardian Angel, so you get much resists against AD and AP. If you are dead you get a second chance for example to kill someone in your base who tries to finish your Nexus and you are the last one alive in your team.

Your skill order is: E - W - Q.
The E damage is the core ability for this build and W gives the needed movement speed to poke them down if they try to escape.
The Q is not that important, just to avoid damage from auto attacks like Tryndamere or to block Garens Q attack.

Here I choose Thunderlord's Decree for the early poke. You can do two attacks and than Q your enemy so the Thunderlord's Decree damage will get triggered. Also important is the bonus attack speed to reach 2.5. Oppressor is good for a fight where you throw a shroom into your enemy so he will get slowed and you deal more damage.

The runes give you also attack speed for the early poke and farming. The bonus health is good for late game and you can suffer more damage without dieing that fast. But why magic resist? Because we will not build any magic resist items so its needed to have it in our runes.

This build is a lategame build. You firstly will need your core items to compete with two enemys at the same time. If Teemo gets slowed or stunned he is pretty helpless with a low chance of escape. And All-ins are a big problem for him, because its a DOT build and not oneshot like Riven if she is fed or Rengar.

Personally I think this build gives many potential for the late game. First you can push very fast you lane or defend your own tower. The second point is that you can simply take the enemys carry out with blinding the ADC or camping in a bush and kill the MID-laner very fast. Also you can hit more than one enemy at the same time. If you choose Teleport and all the enemys are trying to infiltrate you base, but you have some minions at bot or top lane you can teleport to there and push them down faster (happend 2 times: we just had the Nexus left but I pushed four towers, one Inhibitor and the enemy Nexus while my team was defending our base).