In order to build and install the lib and tests using the sdl backend do the 
following:

$tar -xzvf libstk.tar.gz
(note http://www.libstk.org provides instructions for accessing the source via CVS, this is the preferred method as the codebase is being updated at least daily)

$cd libstk
$./autogen.sh
$./configure --enable-sdl --enable-logging --enable-tests
$make

If everything went well, install the library
$su
$make install

(get all the configure options using ./configure --help)

That should do it
if not, check that you have the libs installed in
    /usr/local/lib/libstk*

and the header files in
    /usr/local/include/libstk-#.#.#/libstk/*.h

run the test apps in test/ or /usr/local/bin

let us know how it goes on the mailing list, see http://www.libstk.org

Known Bugs:
test_app will crash if libpng support is not found.