Have a look at the first few lines of the patch. Uncompress it if necessary. You're looking for something that looks like (but not exactly like):

1--- src/dosbox.cpp      (revision 3990)
2+++ src/dosbox.cpp      (working copy)

Your patch might start with a different file, but it will refer to a location in the DOSBox source filesystem structure.

Depending on how the patch file was generated, the patch may look as above or it may refer to two different filesystem trees. For example:

1--- olddosbox/src/dosbox.cpp
2+++ newdosbox/src/dosbox.cpp

To apply a patch which looks like your first file, navigate to your DOSBox source directory and run the following command, substituting the appropriate location and name of your patch file:

1cat ../name.patch | patch -p0

If everything works well, the patch chunks should apply with no warnings or issues requiring your response.

The flag -pN strips N levels of path from all filesystem references in the patch file before applying. This allows the second form of patch to apply by stripping off olddosbox and newdosbox from any file names:

1cat ../another.patch | patch -p1

Using -p1 works while -p0 would not (as patch would not find the two subdirectories it's expecting), nor would -p2 as patch would not find dosbox.cpp at the top level of your DOSBox source directory.

In regards to the revision number, do I need to use the same revision number shown in the patch/diff file? This particular patch says (revision 3661). So does that mean I can only use svn 3661 with the patch?

No, you don't need to use the same revision. For each hunk, patch will attempt to find a matching context (lines to be patched along with preceeding and succeeding lines). Only if it can't find a match will it throw an error.