This isn't going to be a full guide, but I will attempt to explain the basics to doing well with Rumble.

Utilization of your Ionian Boots (CD Reduction): Rumble is very well at pushing & avoiding most harassment thanks to his shield. But it is more difficult to burn down the enemy quicker in an exchange with him than some other champions. This is why we have CD Reduction; to spam your Ulti. Though an 80 second CD (Level 1 Ult) may seem like a lot, it is worth it in the long run to use it when it's up. Typically, it takes about two drops to kill someone: The first drop to kill their minion wave, allowing you to engage/damaging them - the second drop to do the same, as well as give you an opportunity to let off your exhaust/ignite/harpoon to demolish any chances of escape, then burning what ever health is left with that convenient Flamethrower.

The small CD Reduction also goes a long way in the fact that you can get in more time against minions due to the fact that your Flamethrower/Shield will be up more frequently.

Rumble is typically a stronger early game opponent, so use this to your advantage. If it is inevitable the you are going to get hit, embrace it. Throw your shield on to absorb the bulk of the damage, also granting you a speed boost, and proceed to melt the enemy down with that little OP Flamethrower.

This champion can be Tanky, AP Carry, and a Nuker. It all depends on your play style. I hope this helps you one way or another! Thanks for your time :)