Can I connect 2 computers to the internet in different areas of my house?

[PoohBearPenguin]

A router allows multiple computers to share a single high speed internet connection.

So you don't need that second router upstairs. Instead you need to connect your upstairs computer to the router downstairs.

Most routers support WiFi. If your computer upstairs does not have a WiFi adapter, you can buy one from the store. If the wifi signal is too weak, you may have problems with downloads or network reliability.

If this is an issue, you have a few other solutions you can try. One is to use a router and adapter with a better antenna. Point the antenna in the direction of the router or computer to help with connectivity. Another solution is to use a pair of powerline adapters. As the name implies, these are network adapters you plug into a normal electrical outlet, turning your house's power lines into network cabling. The adapters come in a pair. One goes near your router and the other goes near your computer upstairs. Then use a plain ethernet cable to connect the adapters to your router and computer. That's it. The adapters and will do the rest and your computer will get its internet connection settings from your router downstairs.