Name resolution on home LAN?

To resolve Avahi hostnames, other computers should have libnss-mdns installed.

Another option, if you are the network administrator is to distribute a private DNS address by DHCP (I your computers are configured by DHCP). For a small network, dnsmasq is good combined package (DNS+DHCP). It allows you to serve simply your /etc/hosts to the network.

In mixed network environments you can do this with name resolutions from Avahi/Zeroconfig that would resolve in Mac-OS as well as in Windows (when Bonjour is running). See also this answer.

In all recent Ubuntu installs you can use hostname.local and it just works. I believe this means mDNS is set up automatically, but as it's always just worked (except with some routers in some hotels, where I'd get a notification about it being disabled because of a broken router), I haven't had to dig in.