Does generating an address reserve that address on the network then? Or are you just mathematically validating said address?
Once you have a validated unused address, How does one then get it into your wallet ?
It doesn't reserve it in the networks (at least I'm NEARLY sure it doesn't) until you add it to your wallet. What wallet are you using to store your addresses? If you are using a web-based wallet, it varies, but for Bitcoin-QT (the desktop client), go here for instructions:
https://en.bitcoin.it/wiki/How_to_import_private_keysYou can't use it until you import it into your wallet.
However, you don't "reserve it" until you have made a transaction to it in the block chain, then the potential firstbits would be reserved. Firstbits are not an official Bitcoin "thing" but places like blockchain.info and firstbits you can look up an address with the first part of the vanity if your address is the first one used in the blockchain.