Hi JWGaudette,
We see you're looking for some help with locating where playlists are, and how to create one. We certainly want you to be able to view your content as expected, and we'd like to assist.
This page here will have the step-by-step instructions on how to set up a playlist: How to make a playlist in the Apple Music app
The first couple steps on that page will guide towards where to locate them, but just to confirm, you'll want to tap the Library tab in the Music app first. Then, select Playlists at the top here. If the Playlists option doesn't show in the list, amongst the others like Artists, Albums, etc., then tap on the Edit button in the upper-right. Select the circle next to Playlists in this list, if it's not already checked, and then tap Done.
Can you also let us know what operating system you are running on your device?
Take care!