Because tubeless tires require much more effort to break down and reseat, I’m a little hesitant to recommend changing them at home. But if you must the procedure is identical to the method outlined for changing tube-type tires. It’s just a bit more work.
Patching Tubeless Tires
In a word, don’t do it. Although there are emergency patch kits available to plug a tubeless tire, they are only intended to get you out of the boonies and into the nearest shop, where you can replace the tire. All of the tire manufacturers recommend replacing a damaged tubeless tire because cord damage may have occurred as the tire went flat or when the object penetrated the tread.
If you must plug a leaking tubeless tire to get it off the road, fine. Just don’t ride the bike any further or faster than you must, and replace the tire as soon as you can. My feeling is that if the object did not cause the tire to go flat, then remove it and keep riding. It’s extremely unlikely that the nail or whatever went in any further than the tread. However, if the object did any substantial damage to the tread itself the tire should be replaced as a precaution.
Find also how to maintain wheels and tires