"Mining" is the slowest and the most difficult way to get crypto-coins in a timely manner. Mining for crypto-coins is the process in which your computer is used to maintain the block chain that records all transactions of that specific crypto-coin, in exchange for a payment of the same crypto-coin. After processing a block your wallet will recieve a nice sum of coins if you are the one who manages to actually finish the block. This is a very competitive area and there is a chance that you might not even receive any payment after all of your hard work because your luck wasn't good enough. The bright side to mining for coins is that it's free except for the electric bill that you will recieve for having your computer running for an extended period of time.
There are a few ways to increase your chances of success however they aren't always free and can be quite costly. There is specialized hardware that was made just to increase the processing power while lowering the power required to run it. These allow you to mine much more effectively and have a much greater chance of receiving the payment at the end of a block. You can also have more than one computer mining at the same time to increase your chances but this doubles the amount of electricity you will use. The least costly way of increasing your chances is making use of something called a mining pool.
A mining pool is exactly what it sounds like, a group of miners working together to process blocks at a faster rate. These mining pools are usually run by one person but can have a large number of people working in them at one time. In order to become part of one of these pools you must go to that specific pools website and make an account. The profit for completing a block while being a part of a mining pool is split between all the of the miners currently in the pool. This process results in a much slower rate of acquiring the cryptocoin of your choice but it allows you to have a steadier flow.