Applying patches is usually easy:

% cd $sources
% patch < $patchfile

The trick is getting the current directory matched up with the filename listings inside the patch, using the -p option to strip off pathname components.

In the case of the empeg kernel source patches, there are two leading pathname components (up to and including the second slash) that should be removed (-p2).

Combining this with bzcat we get:

% cd empeg-kernel-2.2.12-rmk1-np12-empeg18
% bzcat $patchdir/empeg-kernel-patch-beta8c-beta9a.bz2 | patch -p2
% bzcat $patchdir/empeg-kernel-patch-beta9a-beta9b.bz2 | patch -p2

Cheers,
-v