I have no idea where to start in all honesty. If I make a phone app, for example, how would I go about only allowing people with a university (college) email address to sign up? Would it be as simple as verifying that the input is in fact an email address and then just sending a verification code to that email address?
Yep. Send confirmation codes, activation links, or whatever only to .edu addresses -- and other specific, whitelisted addresses or domains as-needed for development, testing, administration, etc.