The secret key is only used for signing and is never passed in the request. Used in combination with nonces and time stamps you can make a secure API that isn't susceptible to replay attacks.
It's hard to be specific without knowing what you're doing. If you have an app that connects to a third party API like Twitter, that's one situation. If you have an API that other app developers will connect to - that's a second scenario. And third is if you have an API and you write your own app to connect to it.
OAuth handles all three of these scenarios but in #1 you are a consumer, in #2 you are a provider and #3 you are both.
Check out 3-legged oAuth for an example of how to allow apps to talk to your API on behalf of a user, without that user having to give their password to the app. It's actually pretty interesting, clever and simple all at once!
HTTPS encrypts the traffic - making it difficult to sniff. It doesn't actually provide authentication though.
But, at least if it's implemented correctly and not maliciously, the app doesn't ever see your password.