The GNU version of patch describes the option -p as follows.
-pnum or --strip=num
Strip the smallest prefix containing num leading slashes from each
file name found in the patch file. A sequence of one or more adja-
cent slashes is counted as a single slash. This controls how file
names found in the patch file are treated, in case you keep your
files in a different directory than the person who sent out the
patch. For example, supposing the file name in the patch file was
/u/howard/src/blurfl/blurfl.c
setting -p0 gives the entire file name unmodified, -p1 gives
u/howard/src/blurfl/blurfl.c
without the leading slash, -p4 gives
blurfl/blurfl.c
and not specifying -p at all just gives you blurfl.c. Whatever you
end up with is looked for either in the current directory, or the
directory specified by the -d option.
The BSD version describes this option similar, except that the last paragraph is slightly different.
and not specifying -p at all just gives you "blurfl.c", unless all
of the directories in the leading path (u/howard/src/blurfl) exist
and that path is relative, in which case you get the entire path-
name unmodified. Whatever you end up with is looked for either in
the current directory, or the directory specified by the -d
option.
In practical terms this means that if you have a patch starting with
--- doc/Makefile.in.orig 2010-01-25 00:32:06.000000000 +0100 +++ doc/Makefile.in 2010-02-13 22:07:07.508968660 +0100 @@ -272,11 +272,11 @@ ...
on a BSD System you can simply say
patch < patch-doc-Makefile.in
and it will apply to ./doc/Makefile.in; on GNU Systems, patch will try to apply the patch to ./Makefile.in.
Summary: On GNU systems always use patch with -p0