Minting happens when you already have the full blockchain downloaded, your wallet is unlocked (for minting only), and you leave it running.  Coins mature after 20 days and are ready to mint but compete with other users on the network.  Coin age and weight are important factors in minting.  You'll see newly minted transactions come into your wallet which take 50 confirmations to solidify.  Generally, if you don't want to mess with the wallet much but you want to stake, you can open your wallet once a month to download the blockchain and earn rewards.  Minting is not required but how else will you STAY FRESH.  

[EDIT] Forgot to mention orphans.  If you see minted transactions come in which turn to question marks it just means that another user on the network was "ahead of you in the line".  In these cases you can either let your wallet run and ride it out, or try minting another time when there isn't so much competition on the network.