What does a vet do for a broken leg on a dog?

This will depend upon which bone is broken, how it is broken, how bad the dislocation is and how old the dog is.

The easiest fix is for a non-dislocated break of a long bone like the radius or the tibia - after taking radiographs (X-ray images) to make sure the bone is in the correct spot, the veterinarian will splint or cast the leg to keep the bone fragments in place. A fair amount of pain medication, time and exercise restriction later and the break should heal up on its own.

A more complicated fix would be for a dislocated break or a break of the end of a bone in an adult dog. This often requires surgery to reduce the break (put the ends of the bones back together in the correct spot). At the same time, the vet may put surgical screws, wires or plates in to help hold the bone fragments in the correct spot. Once again, a fair amount of pain medication, possibly some antibiotics, time and exercise restriction later and the break should heal up and be fine. Any surgical implants are typically left in place unless they start to cause a problem.

Probably the worst break for a veterinarian to see is a crush/dislocation of a growth plate in a young dog. Repair is tricky, particularly because in a crush-type fracture there isn't a big enough piece of bone to put anything back together with - you're trying to plate together pea gravel and grit. Also, the damage to the growth plate often means the bone will stop growing at this end, which can cause significant developmental problems as the dog grows and may result in the dog needing future surgeries to lengthen the bone. Here treatment is probably going to be turfed to a referral or specialty veterinary hospital if this is an option; surgical correction is mandatory and will probably involve both external fixation as well as internal bridging plates and possibly bone graft as well.