Embedding user specific timelines


I am building a site and would like the ability to embed a users timeline into their homepage by logging in. I know this requires Oauth but I’m having trouble finding anything specific to my needs.

Here’s how I’d like it to work:
User lands on my site > user logs in with twitter > users timeline appears on my site.

I expect more than one user to be logged into the site so the timeline has to be specific to the user only.

EDIT: I’d like to do this with php.