I put together a video that walks you through how to log in and has some tips on using Spelling City on a computer or chrome, safari, etc. browser. This should help if your child is unsure of where to click or how to find the current week's word lists (They are always under "lists not in group"). This video is from early 2017 so Spelling City may have a few minor changes since then.
Unfortunately I can't quite make a video showing how to use Spelling City with the app, but I did show both ways in class and we will be using Spelling City in class regularly so I can imagine the students will get very adept at it pretty quickly. Many of them are savvier than I am with technology!