At the outset, I'd suggest looking up the online manual by searching for it using the model number. I'm happy to explain the process in general terms, but it's been a little while since I set it up.
Basically, the adapter looks like it's just a little mini WiFi router, which it is, but it also has other functionality as well. You plug it into a modern computer via USB and then open a browser and go to a specific address (it's in the documentation). There, you can edit the mode you want to use the thing in. So, 'client' mode turns it into a WiFi receiver rather than an access point. You then enter the credentials for your regular WiFi network. Once everything's done, you unplug it and then plug it into your older Mac using the Ethernet cable (provided). It still needs power via its USB cable, but I just use a wall adapter with a USB port if the thing is stationary (this is less of an issue with computers with USB ports). Anyway, once it's all plugged in, make sure you change your TCP/IP settings to Ethernet if they're not already and you're pretty much good to go!
Yeah, it really does work. I use it mainly to easily transfer files from my newer Macs to my older ones. I have a G4 Mac Mini set up as a little file server. It's nice, because System 7 and OS 10.11 can each access it. On System 7, I go through Chooser and type in the computer's IP address on the network (which I've made static), pop my credentials in and then I'm good to go. The adapter is great, though. Maybe I'll make a YouTube video at some stage and share it. All the best if you decide to go this route.