How does admin award a badge

You’ll be able to award them achievements by visiting their user profile via the WP Admin. It’ll be towards the bottom. There will be a dropdown that you can use to select what type to award and once one is selected, the available achievements will display for you.

I can see this drop down menu on my own profile, but how do I get into someone else’s profile. I have been given admin rights by my professor, but I cannot get into someone else’s to do it!

Sounds like you may not have the capabilities required to edit other users, which would be needed. If this is a multisite install, then only super admins have that level, regardless of “admin” status in the sites in the network.