Mining ethereum is an easy 5 step process:

1. Get a computer with a powerful GPU or two
2. Get an ethereum wallet here
3. Download geth from here and run it like this in a cmd window (because if you have a powerful GPU or two you use it for gaming, hence you have a windows machine)
   1. geth.exe -rpc
4. Download ethminer from here and run it like this in different cmd window
   1. ethminer.exe -G
   2. The -G parameter instructs ethminer to use your GPU instead of your CPU, which will be orders of magnitude faster at mining.
5. You are set, you should see something like this

Now for the bad part. I have two GTX 1080 TI and I am getting around 62 MH/s. This means my computer is capable of taking the Ethereum block we are trying to solve, add it a random string and calculate the hash of it to see if the first ten characters are zeroes and therefore win this block. 62 million times every second. 

62 million times per second sounds like a lot! I should have good chances of winning a block once in a while. Taking into account a new block is generated every 15 seconds, I should have good chances..

The problem is that the Ethereum network has a hash rate capacity of around 60TH/s, this means that the number of hashes the network produces every second are one million times bigger than the hashes my computer produces. This gives me a chance of winning of one in one million every 15 seconds. Taking into account that the reward for winning is 5 ETH (approx 1,150 EUR), I have 1/1,000,000 chance of winning 1,150 EUR every 15 seconds if I leave my computer mining.. this does not sound too promising.