To install the base system, I simply followed the instructions in the online Gentoo Handbook.

There was only one problem: the handbook advises you to use mirrorselect to add a list of fast/close mirrors for the package management system. I tried this, but the list it created had loads of IPv6 addresses which wouldn't route on my network, and a bunch of mirror URLs that didn't have the required files. Deleting the GENTOO_MIRRORS= line from the /mnt/gentoo/etc/make.conf file got the downloads working again.

Other than that, everything went smoothly.