how do i find someone on snapchat properly?

If you've got their number saved, let snapchat sync your contacts and check the add friends list, they'll show up there as long as they allow being found by phone number. Their snapcode works from a screenshot as well, you don't need them standing next to you.

Tap the add friend icon at the top and search their username. Display names work too but there are loads of duplicates, so the username or their Snapcode is far more reliable. If they still don't show up, they've probably limited who can find them in their privacy settings.