Twitter API Authentication

Has anyone set up a Twitter API Authentication to allow a user to log in with their Twitter account (as opposed to just the dev account) and be able to interact with Twitter on behalf of the user?

Would someone be able to help me with that? The trick is that you have to send people to the website to log in which should retrieve a token you then use to authenticate the API calls and be able to do this separately for different accounts (think like building a twitter client).

Thanks in advance.