Creep control techniques

Last hitting
This is a mechanic that will be used to get a good portion of your gold. Delivering the last hit on enemy creeps, heroes and towers.

Creeps are your 'safest' bet on using last hits to gain a good chunk of money. Try to always get the last hit on creeps to get as much gold as you can, this will also ensure they don't get denied costing you precious xp. Try to last hit and only last hit though, auto attacking all the time might make it harder for the other person in your lane to line up his last hits and will push your lane. This will put you in a dangerous position with more chance of being ganked and less chance for them. This has quite a bit too do by how far you or they are away from their tower. Don't wander too far losing your farm by a dead isn't beneficial.

Heroes obviously also give gold when you kill them. Everyone who did damage to en enemy hero within 15 seconds of him dying gets an assist. If you were the hero who delivered the last blow you will get the kill and the bonus gold for it. Also keep in mind that for purpose of last hitting a hero only hero damage is factored in so if a creep kills your enemy right before you hit him you should still get the kill.

Towers give, on top of the normal global gold your team gets, the one who last hits the tower a chunk of bonus gold but that if an allied creep gets the last hit on the tower noone will get it. So try to get that last hit in for that bonus gold but like in most situations consider the situation, getting killed over the bonus gold will probably not be worth it.

Denying
This is the act of trying to prevent your enemies from getting the last hit and so gold. you can start denying creeps when they are under 40% health

Creeps is trying to last hit your own creeps so the enemy won't be able to get the last hit themselves. Along with denying them the last hit the enemy heroes also loses a portion of xp they would have normally gotten for that creep.

Heroes can also be denied. You can only deny allied heroes by means of auto attack, this makes denying a ally pretty tricky as enemy spells will probably be flying around. Always consider the option of this but be careful you don't want to deny an ally that would have gotten away. IT will deny the enemy their gold but it should still cost your ally his gold loss on dead.

Some heroes are able to deny themselves like pudge with his Rot abilty.

Towers Can also be denied as soon as they are under 100hp. This is very important as it denies the enemy team their last hit bonus and their global team gold for the tower kill. That is a lot of extra gold the other team will miss out on. Try to keep a good eye on this as tower who only need 2-3 more hots to die won't be worth much when it comes to defence anyways. Also cause of the big amount of gold the enemies team gets, it might be situationally beneficial to try and deny them even if it seems dangerous. Once again don't be a hero if that might result in a 4v5 teamfight the other team might gain a huge advantage.

Auto attack Animations
Hero animations are undeniably connected with last hitting and denying. Some heroes have better attack animations that lend themselves better it. In a way it is preference but it should normally be easier to last hit with a hero that reacts and applies the damage as soon as possible.

Also consider the fact that when you are playing a ranged the speed of your projectile factors into this. You might need to learn to adjust for this when last hitting and denying too.

Equilibrium
As mentioned earlier it is important to not push your lane too much but try and keep the creeps fighting in approximately the middle of the lane so you never are too far from your tower. creep equilibrium is generally maintained by a balanced appliance of last hitting and denying and on occasions attacking your own creeps before the deny point or attack the enemy creeps to push. Creep Pulling also helps in this.

this is always situational though being pushed might be a bit safer but if the enemy lane is able to slowly chip away at your tower you should push harder. Also access the the side shops might be hinderance on occasions.

Roles and last hitting
Depending on your role in your team you should focus on different things.

Carries should focus most of their attention on getting last hits(without losing track of their surroundings and missing enemies ofcourse)

supports should focus less on last hitting especially if they are laning with a carry. Then it is generally expected that they focus on denying and harassing the opponent so that your carry can last hit without too much harasment himself. Don't starve yourself though, there are always last hits your buddy will never be able to get(melee vs ranged) so don't forgo all last hits just be considerate. Support can also Creep Stack to help their carry farm.