OK, so you want to backup a tree from one partition to another.  That's
what rsyncbtrfs is for. If you want to backup stuff from and onto the
same partition, just use the btrfs snapshot facility (not sure if you
can call that a backup anymore).

Let's learn about rsyncbtrfs with an example:
We have a backup partition /dev/sdb1 which is mounted under /backup.
We want to backup our root /, and our home directory /home/joe. We
assume that / and /home/joe live on separate paritions.

NOTE that the backup partition must be formatted as btrfs.

Here's one way to structure the backup parition:

$ mkdir /backup/home-joe
$ mkdir /backup/sys

So the backup of our home directory will reside under /backup/home-joe,
etc.

Next, we need to initialize each backup directory and we'll be half way
there:

$ rsyncbtrfs init /backup /backup/home-joe
$ rsyncbtrfs init /backup /backup/sys

The first argument is the root of the btrfs partition. rsyncbtrfs needs
this so it can remount the volume as read/write at start and readonly in
the end. All "init" does is that it creates a btrfs subvolume named
"cur" under the given path.

Now let's back it all up:

$ rsyncbtrfs backup /backup /backup/home-joe /home/joe
$ rsyncbtrfs backup /backup /backup/sys      /

NOTE that rsyncbtrfs bind-mounts the source (e.g. /home/joe) under a
temporary directory. This means that any other mount point under the
source path will be ignored. If you wish to include any of those mount
points, back them up separately. If you wish to exclude any from being
backup up, use rsync's --exclude option following all the command line
arguments of rsyncbtrfs. Here's an example:

$ rsyncbtrfs backup /backup /backup/sys / --exclude='/tmp/**'

Here, we prevent content of /tmp to be backed up.

So at this point, you have backed up your home and root directories.
Here is how your backup parition should look like now:

/backup
  |- home-joe
     |- cur
     \- 2010-09-09-12:55:55
  \- sys
     |- cur
     \- 2010-09-09-16:55:55

Obviously, the times and dates would be different. cur directory
contains the latest version of your backup. The timestamped directories
contain snapshots of cur each time after your backup. Thus if you run
backup again, this is how your backup partition will look like:

/backup
  |- home-joe
     |- cur
     |- 2010-09-09-12:55:55
     \- 2010-12-30-20:00:00
  \- sys
     |- cur
     |- 2010-09-09-12:55:55
     \- 2010-12-30-23:00:00

At any point in time, cur would have the same content as the latest
timestamped directory (e.g. cur is same as 2010-12-30-23:00:00).

To take full advantage of btrfs COW functionality, you may want to add
rsync's --inplace flag. This flag tells rsync to only write the updated
data in a file instead of creating a new copy and moving it into place.
Using this flag has several (possibly negative) side effects which you
should be aware of. Consult rsync's man page for further details.
Here's an example usage of this flag with rsyncbtrfs:

$ rsyncbtrfs backup /backup /backup/sys / --inplace

rsyncbtrfs by default adds the following flags to rsync:

 --delete --delete-excluded --no-whole-file

That's it folks. To see the command line options of rsyncbtrfs, run it
bare.