How does mining work I have a basic question on mining.  How does it work?

For example, if I use my computer to mine coins such as litecoins, do those coins go straight into my offline wallet?  Or must I be connected to some online centralised pooling service, which holds to coins until I transfer them to my offline wallet?
You will most likely be using a mining pool, in which case the coin you earn will remain on your pool account until you choose to withdraw it to your local wallet. Most pools support auto-withdrawals (i.e. when the balance reaches a certain threshold).