As with most other action role-playing games, farming is a significant part of the gameplay in Path of Exile. The loots that drop when monsters are killed is one of the reasons why this genre has persisted throughout the years, and it seems that Path of Exile has done well in keeping with that tradition.
But like with most other things in a game, farming in Path of Exile isn't as simple as picking loot up, especially since this game has a much different economic system compared to other games. Therefore, in order to not waste too much time in farming and be as efficient with it as possible, you need to know where to farm, what to farm, and so on.
What to Pick Up
There are quite a few items that are actually valuable enough to pick up, while others should just be left behind. The first item type you should pick up are obviously currency items. As for scrolls, you don't need to if you already have plenty in your inventory so that you can save time.
Only flasks that are good should be picked up, especially those with the "Surgeon's" prefix on them. You should also pick up skill gems, especially those with +Quality since they are very valuable and can be traded for more currency if you don't need them yourself.
You need to get all the rare items that you can get since they can be used for vendor recipes if you don't need to equip them. Uniques are obviously worth picking up as well.
Where to Farm
There are several things to consider when it comes to farming locations. For instance, you should be able to run through them from start to finish as quickly as possible while having the most number of enemies to flow through. The more runs you can do in an hour, the more loot and experience you can get.
Another thing is that you'd want enemies that have a little bit of elemental damage so you don't have to stack resistances to not get hurt too much, and the enemies themselves shouldn't have high elemental resistance themselves so they can get killed easily. They should also come in mobs so that you can use crowd control and AoE skills on them.
To start things off, you have to know where to farm early on. You won't be spending so much time in Act 1, but you'll need some gear to start off with. Farming in The Ledge is a pretty good idea when you're starting out, although spending too much time there would only slow things down.
Once you've moved on to Act 2, you have more options as you're trying to level up more and you'll be switching out gear more. Farming Monkeys in The Forest and Fellshrine Ruins with tons of enemies in them should keep you occupied for a while until you finish the act.
Finally, you get to the fun part that is Act 3, wherein you really start to get the farming ball rolling. There are three areas that are good for farming here, namely City of Sarn, The Docks, and Lunaris Temple & Piety. They have plenty of mobs, which means lots of experience and loot.
Once you're in Act 3, you can stick around for a bit longer and farm what you can until you think that you're ready to move on to the next difficulty level. Of course, you wouldn't want to spend time there for too long unless you're already in the really late levels, in which case you should consider maps instead.