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 apart from Hand of Midas, Devour, Death Pact, or Demonic Conversion, 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 carry as a support do not take any last hits, instead, let the carry get them. 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. Because this decreases your chances of getting last hits, especially if your damage per second is low, and it pushes the lane forward, this is not beneficial. In the late game, however, Heroes often do enough damage per second to simply auto-attack and last hit. Auto-attacking can be useful in any case if you wish to push a lane forward, 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 their 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 a global bonus of gold when razed, but they also give a hefty amount of bonus gold to any hero who manages to get the last hit on one.

Denying
Denying is the act of preventing enemy Heroes from getting the last hit on a friendly unit by last hitting the unit yourself. All allied units can be denied once they fall below a certain percentage of health: creeps and siege units at 50%, heroes at 25%, and towers at 10%. Illusion and summoned units act as creeps in these instances. This prevents your enemy from gaining the full bounty of gold and experience from the kill.

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

Equilibrium
It is important not to 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. This technique is also known as static farming. 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 to 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.

Pushing
Pushing is the act of damaging enemy creeps through auto-attacks or through abilities. Pushing is used to move the creepwave towards the enemy tower, or simply away from the allied towers. Late-game, pushing is used to move creepwaves towards the enemy base to win the game.

Some heroes have abilities that facilitate expedient pushing, such as Leshrac's Diabolic Edict, or Pugna's Nether Blast, which can damage multiple creeps and towers at the same time.

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.

Supports should focus on denying creeps and harassing enemy Heroes so that their carries can last hit without being harassed. Do not throw away the last hitting entirely as a support, because there are some last hits which are impossible for a carry to get (for example, the creep is being killed faster than a carry could possibly get in the attack range).

Supports can also creep stack to help their carry farm.