Currently the users do not have admin rights. I wanted to be able to let them update their own applications (non-microsoft) by using the local admin account at the elevated privilege prompt. What policies do I have to modify in order to accomplish this? Domain environment, windows 7 workstations, windows server 2008 R2 DCs.
Group Policy doesn't let you do this. It's not part of the featureset. You need a third party tool, like Dell Privelege Manager (used to be privilege Authority) or BeyondTrust's product. I've used DPM, and like it well enough, but it takes several goes and testing to get matching for allowed elevations to work. I find it's usually easier to use a deployment system to deploy 3rd party patches I create without user intervention.
You could create a local admin account on their computers and they could enter those credentials whenever they need to install an app. GP won't do this though - at least not the way you want. You could use restricted group members policy to add an account to all admin group on the computers.