I'm not going to write an essay here. I'm showing a way to build, I'll explain some combos, routes, tricks, and play styles. Hecarim is a crazy champion that can be built with a crazy amount of versatility. Most people choose to build him as a full tank or off-tank. These are viable builds, but I have some crazy results and fun with a damage pony. This will not work in every team, so just be careful. With this build, you will be able to dive and kill carries in a matter of seconds.

Pros

Crazy Damage
Burst Any Carry
Insane Ganks
Split Pushing God
Lifesteal and W can keep him alive in a teamfight

Cons

Squishy(ish)
Obviously can't tank for his team

The runes for The Damage Pony are pretty normal. AD Marks for increased damage throughout the game, faster clears, and better early game ganks. Armor Seals are pretty standard on junglers right now: take less damage from jungle and lane creeps, as well as less damage taken while ganking. Either Scaling or Flat MR Glyphs to help you take reduced damage from ganks and fights later. These are important since you will be building little to no tankiness. Movespeed Quints are a must: run faster, do more damage because of Hecarim's passive, and be a speedy pony.

The focus of the Masteries is to get as much damage from the Offensive Tree, get some jungle resistances from Defense, and more bonus MS from the Utility Tree.

Machete and HPs are necessary. For the trinket, I usually go for a Yellow, to help my teams visibility. With Hecarim's E and maybe ghost, a well timed gank is already impossible to stop. Since he can run so fast, you should be in lane before they even see you on the minimap.

Rush a Spirit of the Elder Lizard for the crazy income, sustain in the jungle (He is very mana dependent), and great damage in ganks (True Damage over Time) then full boots as this will allow for better ganks, more damage, and a quicker clear.

The next two core items are Youmuu's Ghostblade and Trinity Force. Youmuu's is a great item for Pony:AD, Movespeed, Crit Chance, Cooldown Reduction, Armor Pen, and Attack Speed. This item is truly integral on Hecarim. Trinity Force gives, almost literally, everything. This item will increase his damage by crazy amounts and I will explain this later.

If you team is just destroying, build more damage. Infinity Edge will increase you damage by quite a bit. Bloodthirster will increase damage as well as give you more sustain. Black Cleaver will increase damage, give you a bit more HP, and more armor pen.

If you find yourself being bursted down too quickly, some good items that still give damage are Mercurial Scimitar (Damage, MR, Movespeed), Frozen Mallet (HP, Damage, Huge Slows), Maw (Damage, MR, shield).

For routes, always start at the bottom buff, then kill Wraiths, followed by top buff. This will end you with level 3, blue, and red. Analyze which would have a better kill potential, top or mid gank. Have that lane back off and get pushed. E to run in behind the enemy and push them towards your laner. Red will help to secure that kill. The key is to find the balance between ganking and farming. It sounds awful, but pick a lane, and camp it. Choose a lane that is not winning or losing, and help your laner win that lane as hard as possible.

In teamfights, use E, Youmuu, and ghost if you think you need it to run straight to their back lines. Skirt the fight until you see a way to get back there. With you combo, you will be able to insta-kill both the ADC and APC (also, maybe the support). Now that the fight is a 3v5, there should not be too much trouble cleaning up the rest of the team. Make sure not to get locked down by CC. To dive their back lines, you need to be sure of your Pony Damage and to not hesitate and get caught.

Hecarim's full combo can 100-0 both of their carries. The key is to first pick which one will be the first target. The first target should be the one with the most cc or escapes. Ex: always kill Viegar first, he has so much cc and damage that can be devastating.

Hecarim's combo: E to get to them. A full E hit with a full damage build will do 360 + ~300(100% Bonus AD) + 226 (200% Base AD from Trinity) + ~600 (if you crit, 50% chance) = ~1500 damage with 1 ability

Q + AA: ~400(Q) + ~1000 (AA damage with a crit) + 226(Trinity) = ~1600 damage with 1 ability and a AA.

Rinse and repeat. As for armor, you have 30 flat pen, plus 5% per time you do damage.

Mix in E and R for bonus damage, sustain, or chasing.

With Trinity procs on your Q every ~3.5 seconds and 1.2 Attack Speed, you will be able to push towers down in almost no time, so do it. Objectives are key to winning games. Your E, Youmuu, ghost, and ult get get you away from a 5 man gank.