How can I connect my PC to Ethernet without a wall socket?

I would recommend looking into powerline adapters. They use your house's wiring to transmit Ethernet, but do check if both floors are on the same circuit because that affects performance. They work better on newer construction, but it could be a decent solution if you want to avoid running cables everywhere.

You might want to check if your PC has built-in Wi-Fi. If it doesn't, a USB Wi-Fi adapter is usually the easiest and most efficient way to get online. It's a lot simpler than dealing with messy cables. But if you prefer a wired connection, running a long Ethernet cable along the baseboards is a reliable old-school method.

You have a couple of options here. You can either go for a USB Wi-Fi adapter to connect wirelessly, or if you're feeling old-school, just run an Ethernet cable from your router to your PC. If you go the cable route, make sure to measure the distance or consider a long enough cable to avoid any hassle.

If you're considering powerline adapters, just make sure to get a good quality one. I've had mixed results with them, especially when the house wiring is old. Wi-Fi is often a more stable choice these days. Just remember to check for a good adapter if you go that route.