Binaries of UrBackup for Raspian are available now here (Update: See the nighlty builds or the “wheezy” folder of Debian of the official releases). Performance isn’t that good on the raspberry pi, obviously. I’d avoid using any kind of compression, for example.
First setup the backup storage. I suggest using btrfs. Plug in a USB-hard disk and create a partition, e.g. using cfdisk. Then install btrfs and create the filesystem:
apt-get install btrfs-tools
Add an entry to /etc/fstab to automatically mount the USB-hard disk:
/dev/sda1 /media/backup btrfs defaults,nossd 0 0
Then mount the hard disk:
Download the UrBackup server package and install it:
dpkg -i urbackup-server_1.2-1_armhf.deb
Resolve the dependencies:
apt-get -f install
Enter e.g. /media/backup/urbackup when it asks for the backup storage path.
UrBackup server should run now and automatically backup clients as soon as you install the UrBackup client on one of your PCs in the local network (from here). If you want to change any settings you should go to the web interface. Let 192.168.0.42 be the IP of your raspberry pi. You can then access the web interface of UrBackup via typing http://192.168.0.42:55414 into your address bar. If you want to access your files you should share /media/backup/urbackup e.g. via samba. There are guides on how to install samba on a raspberry pi (here for example).
Sidenote: I’ve heard that it runs even better on a Cubieboard. It has a SATA-port so the USB-Bottlenet is gone. Unfortunately, they’re even harder to get than Raspberry Pis.