I recently got a new bike with a set of tubeless compatible rims. The stock tires are clinchers with tubes. I'm thinking about putting tubeless on there, but I don't have any experience with them. We have some trees here that drop huge thorns, like nails. They're big enough to go through any tire. When I get the eventual flat, how do I fix the tire? Are there patches? Can you just stick a tube in there?
When putting tubeless tyres on I would definitely recommend that you use a sealant such as Stan's if riding somewhere with thorns. This would be your first level of defence. The sealant would seal up a thorn (or other) hole quickly and painlessly.
You can repair a tubeless tyre with a vulcanizing repair kit, but reseating a tubeless on the trail is very difficult. It is virtually impossible to do without 'shop air' (I haven't tried CO2) so carrying a tube is important for any major leaks.
You can simply run a tubless tyre with a tube until you get somewhere to properly fix the tyre.
Like everything else in the mtb world there are two schools of thought on whether you leave the thorn in or remove it, I would remove it. If you leave it in it plugs the hole but then if you ever do need to put a tube in you risk puncturing that also.
There are tubeless tire boots available that you can use to patch a puncture that sealant won't seal. Really, you can use the standard vulcanizing tube patch kit as well and it's cheaper. Just don't use the glueless type- they barely fix a tube, let alone a tire.
Fixing a tubeless puncture that won't seal is an at home operation, though. You have to clean all the sealant off of the area, let it dry, apply glue, apply the patch, add sealant back and reseat the tire. Reseating the tire without a compressor is a crapshoot- you may get it with a floor pump, you may not.
If you're running tubeless you still need to carry a tube with you for that reason. There's basically no good way to fix a tubeless tire trailside.
In addition to the other answer they also make plug kits similar to what are used on car tires. If it's a large thorn you can pull it and stick a plug in it, usually without having to re-seat the bead, depending on air loss.
I personally like to live dangerously, i ride Mavic UST wheels with UST Maxxis tires and no sealant, no tubes, but i do carry a spare tube in my pack. So far i have yet to flat and I've been riding like that for over a year, 99% all packed trail miles though. So not a big thorn factor on the hard pack.