1) Generate Monero wallet (your XMR private key corresponding XMR address): moneroaddress.org
Save it! Save your Mnemonic seed 25 words, you will need it to recreate your private keys and to use your wallet.
2) Now you have XMR address and you need miner to start mining. Let's download miner and start mining!
Download miner for Windows
Download CPUMiner for Windows 64
Build miner for Linux
Install all dependensies in terminal, git clone miner and build it from https://github.com/wolf9466/cpuminer-multi:
git clone https://github.com/wolf9466/cpuminer-multi.git miner
cd miner
./autogen.sh
CFLAGS="-march=native" ./configure
make
3) Start your miner with the following command, insert your Monero address, generated at the first step