BE AWARE: If you go to play Rumble, just to let you know, he doesn't run off mana, energy or hp. He runs off a cool new system called heat. Each ability costs 20 heat except for his ultimate which costs nothing. the heat stacks up and after a few seconds of not using an ability the heat will decrease by 5 until you reach zero. The up to the heat bar is that when you go above 50 heat (which is called the "Danger Zone") and use an ability, you get an extra bonus for example: his flamespitter in the danger zone deals extra damage and the scrap shield gains a movement speed bonus. When your heat bar reaches full heat (100 heat) you go into overheat mode silencing you from casting abilities but your melee attacks deal extra magic damage. The downside to using "Heat" and not mana some items may not suite you but but in this build I have a mana regen item but only for it's other components.
Rumble can be played in a few ways, a dps (damage per second) champion or a tanky dps. I play him more as a tanky dps so it's much easier to solo top without having to go back to base often. Be aware Rumble has a slow beginning which is very weak so make sure at the beginning to play very defensively, so that means hugging turret if they are harassing and last hitting minions only. But if you play him well and don't feed you'll have no problem mid and late game.
The runes I've selected fit me but feel free to change them when you play Rumble to your fitting, but the runes give me great lane sustainability. The greater glyphs of warding gives me magic resist for the pesky mage harassers with some extra health from the greater seals of fortitude, but most of all the greater marks of insight give me magic penetration and the greater quintessence of potency give you good damage because in this build you don't really get damage items till basically after level 8. All these runes give you great lane sustainability but again you can change this to your liking.
I went with your basic 0/9/21 masteries because they suite Rumble well. In the defense tree I gave it 9 points which gives me your basic amount of magic resist, armor and health for Rumble's lane sustainability which is very important. In the utility tree I made sure to get certain things that you can't exactly get in the store in game like 1 gold per 10 seconds and movement speed, because Rumble is a little slow even with mercury treads and his scrap shield boost. I also put full points into experience gain (5%) because as Rumble if you can get ahead of the other team in levels, your going to do great. Getting the cooldown reduction and spell vamp make him great in teamfights especially with the health regen because you never know when you'll need the extra 30 hp to survive.
Rumble's items are very important as are any champions, I always go with your basic boots, a health potion and a sight ward for ganks by others or junglers, quickly get the mercury treads for some magic resist and tenacity. I then get 2 regrowth pendants for great lane sustainability and because the next item your getting is the force of nature which will give you magic resist, a small amount of movement speed and health regen. Next you'll get the items necessary to buy the Rylai's Crystal Scepter which will inhance your electric harpoons slow allowing you to catch up for kills. Followed by a Randuin's Omen for armor and more hp plus its active which slows the movement and attack speed of near by enemies by 30% for 2 seconds which is very help full in a teamfight. Next item is a Hextech Gunblade for ability power + life steal (great for the flamespitter) and attack damage + life steal because Rumble's auto attack is an attack damage one. This next item is the final piece to this build, Nashor's Tooth which will give you more attack speed so you do more damage when not using abilitys, cooldown reduction for your ultimate and your other abilities and some ability power. It has some mana regen but because you don't use mana it isn't usefull.
The skill sequence I follow is one of the easier ones allowing rumble to dart in and out of battle dealing damage and for chasing. In this build you take turns putting points in his flamespitter and his scrap shield, put one point in for his electric harpoon at level 3 then leave it because it's more used to slow enemies not damage them so at level 1 the ability slows greatly. Of coarse as any champion you put a point for the ultimate whenever you can, so at levels 6, 11 and 16.
Unlike some champions Rumble doesn't depend to much on summoner spells like clarity or surge, but because he's so weak early game I decided to go with some defensive spells, ghost and heal. The ghost is for either a quick get away or a gap closer for a chase and then the heal is for if your about to die. Another thing that's good about heal is that when your fighting and both you and your enemy are at low health they might think they have the advantage you heal at the last second allowing you to have more health then them giving you the advantage.
Thanks for viewing my build guide for Rumble please feel free to comment on this because it was my very first build guide I've ever done so let me know on what I did well on and what i should add for next time. Thank you.