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What is Litecoin?
See the Litecoin Association's introductory video to Litecoin.

Just like its older brother Bitcoin, Litecoin is an online network that people can use to send payments from one person to another. Litecoin is peer-to-peer and decentralized, meaning that it is not controlled by any single entity or government. The payment system does not handle physical currencies, like the dollar or the euro; instead, it uses its own unit of account, which is also called litecoin (symbol: Ł or LTC). This is why you will often see Litecoin categorized as a virtual or digital currency. Litecoins can be bought and sold for traditional money at a variety of exchanges available online.

If you already know Bitcoin, Litecoin is very similar, the two main differences being that it has faster confirmation times and it uses a different hashing algorithm.

What is Mining?
Instead of having one central authority that secures and controls the money supply (like most governments do for their national currencies), Litecoin spreads this work across a network of “miners”. Miners assemble all new transactions appearing on the Litecoin network into large bundles called blocks, which collectively constitute an authoritative record of all transactions ever made, the blockchain.

The way Litecoin makes sure there is only one blockchain is by making blocks really hard to produce. So instead of just being able to make blocks at will, miners have to produce a cryptographic hash of the block that meets certain criteria, and the only way to find one is to try computing many of them until you get lucky and find one that works. This process is referred to as hashing. The miner that successfully creates a block is rewarded with 12.5 freshly minted litecoins.

Every few days, the difficulty of the criteria for the hash is adjusted based on how frequently blocks are appearing, so more competition between miners equals more work needed to find a block. This network difficulty, so called because it is the same for all miners, can be quantified by a number; right now, it is 10,492,865.

Should You Mine Litecoins?
Litecoin mining can be profitable, but only under certain conditions. In the early days people could make a profit by mining with their CPUs and GPUs, but that is no more the case today. The introduction of specialized mining hardware (commonly referred to as ASICs), which can mine much faster and much more efficiently, has made finding blocks much harder with general-purpose hardware.

If you compare the profitability analyses for a CPU, a GPU and an ASIC, you will see that the costs of CPU and GPU mining largely exceed the rewards, and even with free electricity the profits are so small that they are hardly worth the effort.

Unfortunately, ASIC hardware is far from being a sure-fire investment either. Potential buyers should be extremely careful, as various elements should be considered:

Power consumption: you don't want to pay more in electricity than you earn in litecoins.
Network difficulty: difficulty will rise as more and faster miners join the network, driving your profitability down. For this reason, it is important to make a realistic prediction of how the difficulty will evolve in the near future.
Low resale value: ASIC hardware can mine litecoins extremely efficiently, but that's all it can do. It cannot be refitted for other purposes, so the resale value is very low.
Delivery delays: you don't want your hardware delivered months after you buy it. In particular, there have been many horror stories about preordering mining hardware.
Most importantly: always do your own research, and never trust any single source of information. Good starting points are LitecoinTalk.io and the /r/litecoin and /r/litecoinmining subreddits.

Don't feel like investing in expensive hardware? That's fine! Not everyone needs to be a miner. In fact, the easiest way to get started with Litecoin is to buy some at an exchange.
What are Mining Pools?
As we've seen above, finding a block is very hard. Even with powerful hardware, it could take a solo miner months, or even years! This is why mining pools were invented: by sharing their processing power, miners can find blocks much faster. Pool users earn shares by submitting valid proofs of work, and are then rewarded according to the amount of work they contributed to solving a block.

The reward systems used by mining pools can be roughly subdivided into two categories: proportional systems and pay-per-share systems.

Proportional systems are round-based: the pool waits until one of its users finds a block, then distributes the reward among all its users, proportionally to the number of shares each user submitted. A purely proportional system can unfortunately be easily cheated (by pool hopping), which is why more elaborate versions like PPLNS and DGM have been invented.
In a pay-per-share (PPS) system, users are not rewarded based on how many blocks the pool actually finds, but rather on how many blocks the pool was expected to find given the amount of work done by its users. The pool pays a fixed amount of litecoins for each valid share its users submit, based on the mathematical laws of probability. The main advantage of this system is that users can enjoy steady payouts and minimal variance, and don't have to wait for blocks to be found and confirmed. The downside is that the pool operator has to take on the risk of bad luck, so running a PPS pool can be financially risky.
Choosing a mining pool can be a very personal decision, and several factors should be taken into consideration, including features, reliability, reputability, and user support.

What Software to Use?
ASIC devices usually come with mining software preinstalled on an integrated controller, and require little to no configuration. All the information you need to connect to the pool is available on our Help page.

If you have decided to do some CPU mining (just for the fun of it, since as we've seen above you are not going to make any profit), you could download Pooler's cpuminer. GPU mining is considerably harder to set up, and not much more efficient than CPU mining when compared to ASICs. Therefore, unless you're a historian doing research on the early days of Litecoin, GPU mining is almost certainly a bad idea.