There are two potential uses for a Bitcoin NFC ring.
The first is taking payments.
This is very easy.
I recommend doing the following:
Format ring with NDEF text message containing Bitcoin address. Set all lock bytes to 0xFF, to prevent anyone from overwriting your address with a different one. Whenever someone wants to pay you, they can scan your ring.
The second use is making payments. This is a [b:cbrmq5mt]much harder[/b:cbrmq5mt] problem. Why? Because the NFC ring v1.0 is an inactive NFC device, and can not perform arbitrary computation. There is also no way to interact with the ring beyond communication through NFC. This means that your only option, as of now, is to store your Bitcoin private key on the ring and then use that from a more powerful computer. This is a terrible idea, and I don't see any reason for doing this.
Now, there are some NFC chips out there that can perform more advanced computations, and at some point we might get one advanced enough to do ECDSA signatures, which are required for actually making Bitcoin payments from the ring. However, without any sort of meaningful UI with which to confirm or deny transactions, the usefulness of the ring is still limited.
This means that, without doing something clever, the ring is basically useless for making payments, but great for taking them.
Now, if security isn't such a big deal, and we are OK with having credit card levels of security, a conceivable method of making Bitcoin payments with the ring would be to have a third-party service managing payout. So you scan your ring at the store, the store reads your <third party service> ID, and asks for $X from your account at <third party service>. This isn't terribly useful as of yet, unfortunately.
There are a number of other options involving your ring communicating with some third-party service or oracle software directly, acting as a cryptographic access token to your remotely-hosted account which manages your Bitcoins. This is probably one of the best (currently feasible) options.