Instructions
Download and install No$GBA, a Game Boy Advance and Nintendo DS emulator that supports the microphone and touch-screen functions of the Nintendo DS. You can manipulate the touch screen by moving and left clicking the mouse in the right area of the screen. By default, the bottom screen in No$GBA corresponds with the DS's touch screen. You can move or resize the location of this screen with the add-on program NO$Zoomer. Both No$GBA and NO$Zoomer are available for free at emuparadise.me.
Emulate the Nintendo DS touch screen with the free Nintendo DS and DS Lite emulator DeSmuME. The bottom screen is, by default, the DS touch screen. Left click and drag with the mouse pointer to simulate the effect of the Nintendo DS stylus on the touch screen. You can also resize and reorient the two screens on DeSmuME's "Options" screen. DeSmuME is available for free from desmume.org.
Get the Nintendo DS emulator iDeaS, which uses the bottom window to mimic the DS touch screen. You can reorient and resize the two screens from the "Options" menu if you do not like the default setup. To interact with the game and emulate the stylus, use your computer's mouse and left click the touch-screen window. You can get iDeaS for free from ideasemu.biz.