What's the best way to repair a small hole in a tubeless mountain bike tire?

At home? On the trail? How big a hole?

If it’s around 5mm or less you can use a “bacon strip” tubeless plug. If it’s larger you are probably going to want to glue a patch to the inside of the tire. Proprietary plug systems are similar to bacon strips for utility just quicker & more expensive. A plug of any kind can be considered a forever fix.

Sidewall slash? You might be lucky by sewing the cut with dental floss and then patching from the inside but also be prepared to let it go and buy a new tire. Your risk vs cost calculation is your own. I don’t want to be stuck 20km from home with an unusable tire.