How do I get rid of someone elses apple Id that is not mine? I can"t even download apps on the app store

Ok so I jus got this iPhone 5s from someone my Apple ID and everything is in on iTunes and App Store but when I try to update any apps it says password for that person account

As explained in this thread previously, Apps are tied to the Apple Id that downloaded / bought them, and will forever require that Apple ID to update.

If you are being requested for the original owner's Apple ID, that means there's at least one App there that was downloaded with that person's Apple ID, and that person did not correctly wipe the iPhone to remove all apps and data from it, and now its asking for his password.

The Person you bought it from should have done this:

What to do before selling or giving away your iPhone, iPad, or iPod touch - Apple Support

I suggest you do it yourself, assuming the Apple ID in Settings->iCloud is your own, and not the original owner's. Otherwise you will not be able to.

If you can contact the original owner, ask them to follow the steps in that support document, to correctly remove the iPhone from their account.

Beyond that, you could attempt to delete the offending App if you can determine which one it is. You may need to update Apps one by one until you find it.