Creep control techniques

Last-hitting
Last-hitting is a technique where you (or a creep under your control) get the 'last hit' on a neutral creep, enemy lane creep, or enemy Hero. This is the only way to get gold from creeps, and gives much more gold than otherwise when done to towers or Heroes.

Creeps are your 'safest' bet on using last hits to gain a good chunk of gold. 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. Supports 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 also give gold when you kill them. Everyone who did damage to an enemy Hero within 15 seconds of his death gets an assist. If you were the Hero who delivered the last hit you will get the kill and the bonus gold for it. If your tower or one of your team's creeps gets the last hit on an enemy Hero, the gold is split between all Heroes who got an assist. If only one Hero hit the enemy before your tower or creep killed them, that Hero gets the credit (and the gold) for the kill. If no allied Heroes assisted in the kill, the gold is split evenly among all five Heroes on your team.

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.

Denying
Denying is preventing enemy Heroes 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.

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 sufficiently low health). Allied Heroes can only be denied when they are under certain sources of damage-over-time. Always consider this option, but be careful as you don't want to deny an ally that can escape. Denying a Hero will prevent the enemy from gaining any experience or gold from the kill, but your ally will still lose gold upon death.

The abilities that let a Hero be denied are: Pudge and Alchemist are able to deny themselves using their Rot and Unstable Concoction abilities, respectively.
 * Doom Bringer's Doom
 * Warlock's Shadow Word
 * Queen of Pain's Shadow Strike
 * Venomancer's Venomous Gale
 * Viper's Viper Strike
 * Bane's Nightmare

Towers can also be denied as soon as they are under 10% health. Enemy Heroes 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 the death of a single allied Hero, since it prevents the entire enemy team from gaining gold, although generally it is not.

Attack animations and missile speeds
Shorter attack animations (on all Heroes) and faster missile speeds (on ranged Heroes) make last-hitting easier.

Equilibrium
Is important to not push your lane too much, but try to keep the lane creeps fighting in approximately the middle of the lane so you never are too far from the safety of your tower. Creep equilibrium is generally maintained by balancing last-hitting and denying, and on occasions attacking your own creeps before the deny point or attacking the enemy creeps to push. Creep pulling can also help maintain equilibrium.

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 Blocking
Creep Blocking is a tactic that makes the equilibrium of the lane lean towards your side. This is accomplished by physically blocking your creeps' path with your hero so they take longer to reach the middle of the lane. Since your creeps move more slowly, 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 of course).

Supports should focus less on last-hitting especially if they are laning with a carry. Then they should focus on denying creeps and harassing enemy Heroes so that their carries can last hit without being harassed. There are always last hits carries will never be able to get (melee versus ranged), so supports need not forgo all last hits.

Supports can also creep stack to help their carry farm.