How do I actually get photos into an album once it's created?

Open the album and go into its File Manager, then hit the Upload Photos button up top. You'll get a choice of two main routes: "Upload Complete Folder" if you want to keep your existing folder structure (ceremony, reception, whatever) and dump a big set in one go, or "Upload Selected Images" when you just need to add a handful of specific shots. There's also something called Relay Upload for assisted transfers, which is worth knowing about if you ever have a truly massive delivery and want help getting it up there.