Is there anything special I have to do to have textures bigger than 256x256? And also is there a way that I can detect whether or not the users card supports textures above 256x256? For instance, is here a way that I can do something like NeHe did in lesson #25 do detect it?

you can get the max texture size with:
glGetIntegerv(GL_MAX_TEXTURE_SIZE, int *var);
i think this shloul work. this function returns the max size of your gl implementation.