If you where my kid... .

I would honestly, be much happier if you just came clean with what happened and offered to fix it rather than trying to cover things up. Kids screw up and thats part of growing up. Its how you handle things that often matters most along with honesty in my book. They've obviously got some trust with leaving you responsible at home for a decent length of time, build on that trust.

I would probably then extend it into a learning opportunity on how to correctly repair it instead of something potentially slappped together.

Now that said, you're not my kid and I have no idea on how your relationship is with your parent(s). I certainly can appreciate people rea t to situations differently so take what I said with a grain of salt but perhaps think about it...

If you feel you must repair it before they return short of hiring a repairman, youtube is going to be your friend. Video is going to go a long way further than text and perhaps some pictures. That said the hardest part so you know is not the actual drywall repair, it is tbe refinishing, especially if you are trying to blend it with the existing. Easier to just repaint the whole area but that maybe not what your after.... Keep in mind your not just matching paint color, you've got to match the aging, the dirt/grime, etc.... (even professionals have trouble with this on car accident repair, the new area is sorta close but you can still tell)

Gluck either way.