Creep control techniques

Last hitting
Last hitting is a technique where you (or a minion under your control) get the 'last hit' on a creep or other opponent. This is the only way to get gold from creeps, and gives much more gold than otherwise when done to Tower or Heroes.

Creeps are your 'safest' bet on using last hits to gain a good chunk of money. This is the primary source of gold in Dota 2. It is always desirable to get a last hit on a creep, although when laning with a partner it is often polite to give him some last hits, and is quite important when he is a Carry. Support should focus on harassing enemy Heroes and denying your own creeps.

Auto-attacking refers to the usually less desirable technique of simply letting your hero attack at will. Since this rarely results in getting the last hit, this has very few benefits. In the late game, however, heroes often do enough damage to simply auto-attack and still gain all the last-hits. Auto-attacking can be useful in any case if you wish to push a lane forwards, since it kills enemy creeps faster. This is especially useful for killing towers. In the early game, however, pushing towards an enemy tower is considered dangerous, as it leaves you far from your own towers and makes it much easier for enemies to Gank you.

Heroes obviously also give gold when you kill them. Everyone who did damage to an 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 no-one 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 by getting the last hit yourself. This 'denies' your enemy the gold and some experience from the kill. 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 gold, enemy heroes also gain less Experience from the creep.

Heroes can also sometimes be denied. Most heroes can only deny a friendly hero by attacking them manually (one exception to this is Tiny, who can deny any friendly unit using Toss as long as they have low enough health). Friendly heroes can only be denied when they are under certain sources of damage over time, such as Doombringer's Doom. Always consider this option but be careful as you don't want to deny an ally that would have gotten away. Denying a hero will prevent the enemy from gaining any experience or gold from the kill, but your ally will still lose gold from dying.

Pudge is able to deny himself using his Rot ability.

Towers can also be denied as soon as they are under 100hp. The enemy team members will gain far less gold from a denied tower. It is nearly always beneficial to deny a friendly tower if at all possible and as soon as possible. In some cases it can even be worth a single hero dying for, since it prevents the entire enemy team from gaining gold, although generally it is not.

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.

Creep Stopping
Creep Stopping is a tactic that makes the equilibrium of the lane lean towards your side. This is accomplished by physically blocking the creeps' path with your hero so they take longer to reach the middle of the lane. Since your creeps take a longer path than enemy creeps, they will meet closer to your tower, making it safer for you to farm, and more risky for the enemy.

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.