For serious off-road vehicles, locking differentials are very much useful. The parts of the locking differential are very much the same as that of an open differential. However, there is an added electric, hydraulic and pneumatic mechanism in the locking differential that locks the two pinions together.
The mechanism is usually activated manually by a switch. Once it is activated, the wheels starts to spin and same speed. In cases that one wheel ends up off the ground, the other will not care. Both of them will continue spinning at same speed as usual as if nothing has happened.
When you need help with differentials, the internet is a great source of help. You can find differential rebuild kits online that will help you DIY rebuilding your differentials. If the DIY thing is not for you, you also have the option to seek help from specialists. They shall help you fix the problem and get your car or truck moving again in no time.