system recovery

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how do I boot from a backup?

BackinTime does not make full system backups by default, so recoverying from a snapshot is probably not possible I am afraid.
You should reinstall the system and then you can recover the folders that are available in the snapshots. You can do a full recovery by starting the program, select a snapshot from which you want to recover. Select the folder that you want to recover in the Backup folders section, go one folder up by pushing the arrow. Select the folder in the files section and push recover. If you have additional included folders you can do that for each of them. Might take a while, and it overwrites data without warning!!!

Hope that was an useful answer.

thank you Bart, but what if I do backup my entire file system
is it possible to boot from the snapshot without first installing the entire operation system?

Oops, I just thought about it and gave an incredible wrong answer. I sort of imagined that the snapshots were stored on a separate harddisk (e.g. external), however that is of course not necessarily the case. If they are stored on the same partition will reinstalling the system (and formatting) delete also the snapshots. If they are stored on the same partition you will first have to recover the system. If they are stored on a separate might that be not necessary, if you make sure you do not overwrite the snapshots.

It is not possible to boot from any of the snapshots, at least not in a way that I am aware of, although in principle it should be possible to pursue grub to take one of the snapshots as the root of the system.

If you want to backup the whole system, you should start backintime as administrator, select / in the include folders, and delete all the standard patterns (as they skip all the hidden files (.*) which are mostly configuration files, and the trash files. The only thing to exclude is the backup folder itself of course, and you should leave out the /dev, the /proc, the /sys, and /tmp (they do not contain necessary information or are made as the computer starts, change a lot and therefore take unnecessary space on a backup). This should end up in a full system backup.

But why would you want that? Normally all the files that you modify as a normal user including any configuration files are stored in your home folder. Normally the rest of the system is exactly like how your distribution distributes it: what means that by reinstalling the system you do not lose anything, even not your personal configuration of all the programs you use. You could lose additional programs, however installing them is often not really much of a hassle, and it cleans up the space from programs that you installed once, but were not what you expected. But it is up to you of course ;-)

What you could do though in case of a disaster as you describe: take a live disk (like the ubuntu installation CD), mount your snapshot partition (if not located on /, might become /media/disk), mount your / partition (might become /media/disk1), mount any additional partitions (like /home) under the / partition that you just mounted (eg. under /media/disk1/home), and then copy the whole snopshot recursively to the mounted / partition (so /media/disk1) by the next command:
sudo cp -a /media/disk/backintime/20090731-215002/* /media/disk1/

That should restore the whole system then (if the backup did contain everything), without the need to reinstall... however I did never do such a thing...