After installing Arch on my Raspberry Pi, internet worked out of the box: I could plug it into the router, turn it on, ssh in and start downloading things. But the router is in my housemate's bedroom, which isn't ideal. If I want the Pi to be connected to the internet in my room, I need it to be connected to my laptop. (Another option would be a USB wifi dongle, of course.) This is how I did it. Much credit goes to the Ubuntu wiki's Connection sharing page.
I should disclaim that I don't fully understand networking stuff, and some of what I say might be wrong. I also didn't write this as I was going; so while I've consulted my browser and shell histories, it's possible I've forgotten some steps.
My laptop is running Gentoo, and this is where most of the work has to be done. It connects to the internet through wifi, on interface
wlan0. The ethernet port is
eth0 is also the name of the ethernet port on the Pi.
Step zero: plug ev