How is a Ripple address constructed? Is it similar to how a Bitcoin address works albeit with a different net byte, or are there some more differences?
The structure of the address itself is basically the same as they way they're done in Bitcoin. Not only is the network byte different but the alphabet is different.
However, the client generates accounts very differently from the way it's typically done in Bitcoin. The client begins by generating a random 128-bit seed. This seed is shown to the user and they are asked to write it down to ensure their funds are never lost.
Any number of public/private key pair and accounts can be generated from this seed. And accounts are generated from those public keys.
Of course, Bitcoin clients could generate accounts this same way and I believe that at least some do.