Teemo is a weird jungler. He falls in to a gray area between a utility champ and a marksman. He plays for late game and destroys melee champs. And plus, post level 6 he has one of the fastest clears in the game with his Noxious Trap. Overall I play him for his ability to tilt and his amazing power farming.

Your path is either gonna be

Red

Blue

Gromp(smite)

Wolves

Scuttle

OR

Blue

Gromp(smite)

Wolves

Red

Scuttle

Both of these paths deny any vertical jungling by going buff to buff

Teemo is NOT AN EARLY GAME JUNGLER

he is a power farming jungler.

He does not look for early ganks or go for invades.

he is super weak early in a 1v1 but can 2v2 very well.

so your game is gonna look like this

once your pathing is done look at over-extended lanes and gank them, these are your only ganks early. if you don't find any ganks go back to farm.

Be sure to track the enemy, this is what separates a good jungler from a great one.

Plan your backs as well. make sure you are'nt backing and leaving an overextended lane alone.

Give up first drake as well unless fed. by the time second or third drake comes in you'll have your runic echoes and nashor's tooth so you can take whatever comes at you.

CHALLENGING SMITE

Take challenging smite in to matchups where you wont need to catch up to them. The burn is nice for 1v1's as well
CHILLING SMITE

Take chilling smite into matchups where you will need to catch up to kill them or to kite them. also take for burst.

Teemo is akin to shaco. Tilting, slippery, annoying and does a lot of damage. If the enemy sees a fed teemo jungle, they'll flame their jungle so bad that he'll play even worse. Use this to your advantage

Please check out my man Manco1's stream. He inspired me to play and refine teemo jungle
go give him a follow and tell him i sent ya

Much Love

Bit