Leveling up is a very important development trait for your character as it is the main way to advance through the passive skill tree and also a requirement to equip higher level gear. The basic premise for any ARPG is to kill monsters over and over again, but there are ways to make the killing more efficient. There is only one way to technically increase your experience gain and that is though the Chitus' Apex unique, so don't bother looking for magic/rare items with increased experience mods as they simply aren't there. The current level cap for Path of Exile is 100 but the developers have stated that it will take a long time for a person to get there, in fact there is only one guy so far that has managed to do it according to the softcore ladder.
Let's go on shall we?
Do not waste time trying to kill every single monster in an area; it is far more beneficial for you to kill the "big groups" and then start a new instance than to waste time trying to find stragglers. Remember that you can ctrl+click on an entrance to bring up the Instance Manager to quickly start a new instance.
Using AOE (Area Of Effect) skills goes hand-in-hand with the previous point, so make sure you pack one of these in your arsenal. As a general tip try having one AOE and one single-target skill available at all times.
Rarity = More Experience
Monsters that have a magic, rare, or unique rarity will give more experience when killed than their regular counter parts which is why you want to make it a focus to hunt these down.
Upgrade Your Gear
Having better gear will not only increase your survivability but also make the actual monster killing faster. Always make sure you have the best gear for your level, and if you don't, give trade chat a look. Unless you are playing "self-found", trading with other players is the best way for you to upgrade your gear simply because the chances of dropping gear that is both applicable for your character AND better than your current piece is very low.
Dying will not only force you to run back and waste time, but it will also take away a portion of your experience in Cruel and Merciless. This experience deduction can become a huge setback if it happens frequently as you can find yourself loosing more than you are gaining. Don't overdo it with the monsters; there is a difference between trying to be efficient and being stupid, so always keep the monsters you are fighting to a manageable amount.
Don't Be Scared To Repeat The Same Areas
There is no shame in repeating the same area over and over again if the next one is just too hard for you. The side areas are very hard especially in Merciless so I frequently find myself doing the same area repeatedly just to get some better gear or more levels before attempting them.
Some areas are also better suited for your build and play-style than others. For example when using a ranged character I prefer locations filled with slow-moving melee monsters such as zombies, but as a melee guy I would pick locations with fast moving monsters that close in on you so that I wouldn't have to chase them.
Playing in a party can be beneficial for your leveling goals. Each additional party member will increase the monster's experience by 50% which is then split amongst the party, so you actually get less per kill but because it is faster and easier you end up getting more per hour. Note that you need to be within two screens of a kill in order to get experience. In order to encourage people to actually play together and not go their separate ways, GGG implemented a 30% additional experience bonus for players playing in the vicinity of other players. You will get the most experience if you are the same level or higher when compared to your party members since your level is used to determine your share.
More information about how experience is split when in a party can be found on this wiki page, right at the bottom.
Summoners Good, Summons Bad!
Summoners are bad news for people trying to level up fast. It may sound like a good idea to farm summoned monsters (I mean they never stop coming right?), but the thing is they don't give any experience or drops. When you came face to face with a necromancer kill him as fast as possible, or better yet, don't go in areas where they spawn.
Monster Level And Experience
If your character level is too much higher or too much lower than the area's monster level you will be penalized in terms of experience. This is a very important thing that you need to be aware of so that you will only play in areas where you are getting 100% of the experience. A full explanation of this mechanic can be found in our monster level post (at the bottom).
It goes without saying that increasing your movement speed will increase the rate at which you clear areas. Movement speed increases can come from the passive skill tree as well as from mods; try to aim for something like 25%. There is no cap on movement speed.
What Do The Others Do?
Many streamers and YouTube guys have come up with "paths" that you should take to level up the fastest, such as this one. I don't have many specific links but searching TwitchTv or YouTube brings up many hits; good luck!
As a final parting note I suggest you check out this video uploaded by Kripparian, a very popular gamer. It contains useful information relevant to this topic.