I'm sure most of the folks from SMWCentral will already know this, but I'm including this for people who may not know ^^
You'll need a few things to play this game:
-Floating IPS: https://www.smwcentral.net/?p=section&a=details&id=11474
-An SNES Emulator (For instance, SNES9x or Bizhawk, or the SNES9x Chrome extension)
-A clean Super Mario World ROM (.smc or .sfc) (I can't provide a link to a ROM, but a google search should do you well.)
-The Peach's Adventure patch (.bps)

1. Run Floating IPS (Flips) and press 'Apply Patch'. In the window that pops up, locate and select the 'Super Mario Bros. Peach's Adventure W6 Demo.bps' patch, and press Open.
2. A new window will pop up. In this window, locate and select the clean Super Mario World (.smc or .sfc) ROM and press Open.
3. One more new window will pop up. In this window find where you want to save the new ROM. It's default name is 'Super Mario Bros. Peach's Adventure W6 Demo.smc', but you can name it whatever you want, as long as the filename ends in either .smc or .sfc. Then press Save.
4. If everthing was done correctly, Floating IPS will then tell you that the patch was applied succesfully, and you can close it.
5. Then, run the SNES emulator of your choice, locate where you saved the Peach's Adventure ROM, and you're good to go!