Your main role in the game is to mess with the enemy team as much as possible.
Start off with a level in E and running into their territory. Place a ward and camp by the bush in river. When you see your team comes in behind you, what you wanna do is when your team engage you flash over the wall and do a devastating charge at the enemy mid laner- pushing her into your team and then exhaust her.

In your lane you want to position yourself in your side of the bush with a vision ward. When you hit level 6 you use your ult on the enemy adc, then push them back with you E abillity simultaniously exhausting them. Rendering them highly vulnerable against your adc.

Later in the game you have awesome warding potential because you can roam the map freely picking off enemy wards and get back to lane wihtout losing much exp because you are so fast.

In teamfights you instantly charge on the enemy carry. You do this by wait until someone throws their cc, then jump with E or ult. Because you are hecarim, you can simply charge and push away the enemy tank and then let your jungler protect the carries while you use your ult to cause chaos in the enemy back line and charge at their adc. When arriving you instantly activate W giving you some sustain while attacking and pushing back the enemy caitlyn from the fight by spaming Q.

Don't forget to place down a ward in the middle of the teamfight so that you can teleport back and chase down the one who escaped with low HP!

With your insane movement speed you dont need to care about your enemies when running around the map, ganking or farming. You can even juke them around bushes or steal baron if you're sure of yourself!