If you're using a true UST tubeless tire on a UST rim, you may not require sealant. If you're running a "dry" tubeless system, you can use different techniques (such as superglue) to patch a puncture. If you're using sealant in your tire, go to our "fixing tubeless tires with sealant" page.
You may be asking yourself, " What kind of moron rides tubeless without sealant?" Well, very few riders do. It's usually a cross-country racer who wants to eliminate as much weight as possible from the wheels. They're taking a chance that they won't find a shard of glass for the 90 minutes they're on the trail.
Note the "stress marks" on the sidewall of this tire. Flexing of the sidewall is separating the cords from the rubber. (This tire was primed to blow, because it's a light-weight non-tubeless tire, run with low pressure.) Sealant won't protect you against this type of tire failure.
Let all the air out of the tire and remove it from the rim.
Pinch the tire to expose the inside of the cut or puncture.
Clean the area of the puncture. I recommend against sanding, because you may expose the tire's cords, making the repair less secure.
Apply a thin layer of patch glue.
If the tire has been on your bike for a while, you may be able to seal the bead again with a good floor pump.