Excellent build thread. Thanks for sharing. I think the research you did will lead to more than a few new basking platforms for our

friends.
The PVC cement (available at any hardware store) has an applicator on the cap. The underside of the cap has a little ball/brush thingy attached to it.
you'll want to buy two things. A small jar of PVC cleaner (oatey yellow can) and a small jar of the all-purpose cement (red can). You aren't using this for water flow so you can skip the primer (purple can).
Use the cleaner first to remove any of the printing or junk from the pipe. Then the cement...
If you've never worked with PVC cement... practice on a scrap first. Once you apply the cement to one of the pieces....twist and push the next piece into place.
You''ll have about 4-5 seconds to work with the PVC. It's very very very fast and there's no undoing it if you glued it properly.