Update: A real tool is available to do this, and it works in 64-bit Vista, so use that instead.

Microsoft is working on a tool to simplify restoring files from backups you made with Windows XP, but it’s not ready yet. In the meantime, plan on scrapping your old backups–as soon as you get Vista running, do a Complete PC backup, and then schedule nightly backups.

If you really need to restore files from a .BKF file, this thread provides guidance. I’ll copy the steps here for reference:

1) create a folder somewhere, call it ntbackup just so you can keep track of
what you’ve done
2) from an existing XP installation, copy these 3 files into the new folder:
ntbackup.exe, vssapi.dll, ntmsapi.dll. Optionally, copy the files
ntbackup.chm and ntbackup.hlp. Do not overwrite any Vista files that have
the same names.
3) run ntbackup.exe. dismiss the error dialog concerning removable storage
if it appears.
4) catalog the backup file as you normally would (select the Restore tab,
then select Tools/Catalog) then select and restore your files. Remember to
restore them to an alternate location using the drop-down box in the
lower-left corner of ntbackup.

If you don’t have a running XP installation, then extract the listed files
from the XP installation CD. If you don’t know where these files are, you
can use search to find them; they will have the same filename except the last
character will be an underscore (e.g., ntbackup.exe will be ntbackup.ex_ on
the CD). i have not done an exhaustive search of every version of XP’s
installation CD to determine their locations.

Since you are (presumably) not running as an administrator under Vista as
you probably were under XP,
1) some extraneous errors may occur during the restore. check the results
of the restore to ensure that you got all the files you needed from the
backup, and apply the appropriate security settings to the restored files
manually if necessary
2) You might need to turn off the option to restore file security. (Hit the
“Advanced” button in the restore dialog).

ntbackup also appears to work for backing up files, but I wouldn’t trust it
to do so correctly without extensive testing.