I have followed all the steps to mine Ethereum and I am currently mining, but where does what I have mined go?
Is it through the address that I was given through Geth?
How do access the mined Ethereum?
Assuming you're mining with your own rig, any mining rewards - paid in ether - get deposited into the coinbase (aka. etherbase) account on your system.
See the following for a thorough description of which account this actually is: What is coinbase?
I believe that if this account hadn't been set up, then you wouldn't have been able to start mining - there would have been an error message.
From the geth console you can run
eth.getBalance(eth.coinbase) to see its current balance.