How to make and apply SVN patch?

Use svn patch.

Case 1: using /usr/bin/patch:

svn diff > $TMPDIR/mypatchfile.patch
cd myOtherCheckOut
patch -p0 < $TMPDIR/mypatchfile.patch

Applies your changes well if there are no added/deleted files through svn add or svn delete

Case 2: using svn patch:

svn diff > $TMPDIR/mypatchfile.patch
cd myOtherCheckOut
svn patch $TMPDIR/mypatchfile.patch

Tracks added and deleted files too.

Note that neither tracks svn moves and renames