We are using google OTP api. It's quite simple:

1) We are generating secret key, which then saved by our service and user.
2) System time of all sides syncronized from the same source.
3) User runs offline generation of OTP code using his copy of secret key and his own system time. Code will be valid for 60s since generation time.
4) User sends OTP code to us
5) We are calling OTP api method, which runs code validation
6) If it's returned true, code is valid and authentication is completed.

OTP api is completely independent from user accounts. It's used by google to implement authentication, but anyone also can use it for own services. And you can use any amount of secret keys simultaneously.