Jungle Order:
I recomend to always go to kill your first monster with your bot laners. Also try not smiting it because that way when you go to your second monster camp you may activate your "w" and smite the monster and gain more hp back.

BTW always be sure to smite the monster meanwhile you have your "w" active because that way you will gain more hp back ,but if you can't it isn't much of a deal,, but if you fight against Red Buff always smite meanwhile you have your "w" ativated.

After this you may wanna go for crab at river this way you won't have to spend any pots when jungling.

Then you should gank if possible. If you can't you should go and do birds or wolves. Continue by killing Blue or Red buff.

P.S.:Try ganking as much as possible.

Warpath (passive): Try using this to your advantage there for when ganking activate you "e" followed by ghost or Yoummus to deal extra damage.

Rampage ("Q"): Spam this ability when killing monsters, champions, etc. Also use this ability to strike down monsters so that when you get to another monster camp you will have the coolddown reduction activated.

Spirit of Dread ("W"): Use this to your advantage by activating it when smiting monster to get all that healing. Also when in teamfights activate it to regen all the damage you've taken.

Devastating Charge ("E"): Use this when ganking. Remember to bump into stuff when the ability reaches 100 stacks to be able to push your enemy the furthest. Also try using the push to your advantage by pushing them waway from your teamates or into them. Take into account this ability works well when escaping enemy champions or for lowering down turrets.

Onslaught of Shadows ("R"): This ablity is extremely good for escaping battles you can't win or to croud control the enemy team. Use it to scare enemies into your team or to scare them off.

Pros of using Hecarim: Hecarim has a fast jungle clear which means he can gank as much as champions like Shyvana, but unlike her, Hecarim can actually gank better due to his "e" and ult.
Also Hecarim is great for crowd controlling and with the right timing of the ult he can assure wins in teamfights even with the score turned against you.
Take Hecarim's speed into your advantage by pushing lanes and escaping from dangerous opponents.

Cons of using Hecarim: If you are new to Hecarim getting the hang of him might be very dificult. In other words you need to due the right thing when ganking because if not the consequences can be fatal.

Jungling:With Hecarim you should start by trigerring "q" twice before activating "w" that way you will be able to hit the monster twice with your "q" and get more health back. You may also start by pressing "e" before attacking the monster camp, but if you do so remember to activate "w" before you bump into the monster.

Ganking : Start with "e" then approach you enemy and spam "q" meanwhile having "w" activated. Use your ult when the enemy is escaping that way you will scare him/her towards you.
P.S. Try hitting your ult towards where the enemy is fleeing to. That way, they will flee towards you due to your ult's effect.

For farming all you got to do is stand in the middle of the minions, then activate "W" and trigger "Q". This way you will not only get healed, but you will have a fast clear great for pushing.

I personally don't like starting fights with Hecarim simply because you will get one shot if your team doesn't enter due to the lack of confidence they have towards Hecarim. You should let champions like Malphite start team fights with his ult so that its is much easier for you to ult and have a secured win in almost any TF.

Hecarim is a champion which doesn't usually gets banned in rank so you will usually be able to use him everytime you want in ranked. Also take in mind that banning championss like Olaf or Shyvana fit great for you and yor team specially because of them being your counters.