The most common cause is either intense stop and go activity over a hard surface (ex: flyball, chasing tennis balls on concrete) or overuse (ex: hunting, hiking, or dog sledding over rough or icy terrain, especially without conditioning). Unfortunately treating sore feet like paw abrasions are not an overnight fix as they are somewhat similar to a blister on the bottom of your feet. Prevention and gradual conditioning will be the best way to avoid pad abrasions. There are products such as Tuf-Foot and Musher's Secret that have been out for a long time to try to either toughen up or protect the foot that be worth trying. Flyball competitors often wrap with vet wrap and tape around the carpus to protect the stop pads and declaws. Please note that unlike horses, dogs have considerable more soft tissue in the lower leg than horses, so do not wrap the vet wrap too snugly and remove shortly after the race. Specially made dog skid boots might be a better alternative.
So what do you do after a long hike or hunting trip and your dog comes up lame? Inspect the feet very carefully, looking for burrs, thorns, cactus needles, ice balls, dried mud, and so on. Keeping a pair of hemostats to pull out the offending object may be very helpful, particularly when trying to grab it without poking yourself. Clean the area thoroughly with soapy water and rinse. If my dogs have a pad abrasion, I like to have them stand in a 2 quart plastic pitcher or small bucket with a warm water soak to remove excess debris and dirt, then stand again in dilute chlorhexidine solution (Hibiclens, which can be found at Walgreens or Walmart). The sore pad can be LIGHTLY bandaged if desired, but the best solution is to crate the dog so they will rest. The issue with some bandages is doing it too tight, which causes swelling and discomfort and even necrosis of the tissue if untreated long enough. If you decide to bandage the feet, make sure to leave at least two toes visible so you can check for swelling and either too warm or too cold in the toes. Some dogs will also shred and eat the bandaging material, which is never desirable. Ask your veterinarian for pain medication for a few days if the dog is especially tender or has difficulty walking. An infant sock can be helpful to taking the dog out to relieve themselves. There are now quite a few brands of booties available to try as well at various retailers.
For pad lacerations, these can be very, very challenging to treat because almost any movement can break them open again. They make take multiple times of suturing and bandaging before successfully healing. Patience and rest is the most important thing with both pad abrasions and lacerations.