the harder plastic screen protector is for the touch screen. both are slightly smaller than the frames that they fit into. it's been awhile since I did one of these, but if I recall, the installation procedure is as follows:
you'll want to try and work in a dust free environment to begin with. the screen and the screen protectors both attract dust like magnets. try moving everything to your bathroom and run the shower (on hot) for a few minutes to steam up the room and cause the dust particles to fall from the air.
then wait a few minutes more for the temperature in the room to return to normal (you don't want your ds all wet with condensation).
applying the screen protector:
peel back the protective covering from one side of the screen protector (this should be the side that easier to peel back) and the thicker of the two protective layers covering the actual screen protector. starting at one side (or one corner), place the screen protector in place and moving from that side (or corner) work out any bubbles with your fingers (I use a soft cloth over my fingers) as you move across the face of the screen slowly.
you're trying to push any bubbles from where you started to the edges where they have an easier time of escaping from between the ds's screen and the screen protector.
once, the screen protector is in place, use the pull tab to release the protective coating on the external side of the screen protector.
good luck!