To Start a fight, Begin running towards your enemy with your E ability. To deal maximum damage, Combine your E ability with the spell Ghost, As it makes you run faster, According to your passive, The more movement speed, Means the more damage you deal. Note that the next basic hit will knock the enemy back. So try to prevent their escape by passing them with your high movement speed, And only then striking them.

The W ability summons a life stealing aura which will follow Hecarim for a short period of time. To make the most out of this ability, Use it when there are many minions or enemy champions around (the more enemies in your aura, The better the life steal would be).

Your Q ability grants you what i call, A "free swing" simply because Hecarim will swing his spear and hit all nearby minions and enemy champions. The ability stacks, Which means that if you hit a minion or an enemy champion, The cooldown on the ability is lowered. The ability itself is not very powerful (not much stronger than your basic attack), But can grant you a high advantage over your enemies, Since it does not take any casting time (the ability will be done in between the basic attacks).

Hecarim's ultimate (the R ability) allows him to launch towards enemy champions, Fearing them away from him, And dealing damage. If you would like to prevent an enemy's escape, Use your R ability to launch and pass them, Which would make them run backwards (towards your team, Or just away from their turret). The ability is also useful in making your escapes, As it works through walls and terrains. Hecarim is not an easy champion to escape, Or catch up with, So you wouldn't normally use it to escape, Unless stunned or slowed, Then i recommend using it to prevent a death.

I will soon explain the thoughts behind the items.