How do you perform the TGU? Basically you go from lying flat on your back to an upright standing position to back to your back. Like most exercises when you write it out it looks like the most complex thing out there so here are some of the basics with a few videos that explain the finer points of the movement.
Hip roll: You will roll onto your left hip and support your weight on your left elbow. From that position you will continue to push up until you are on your left hand. All of this is done while keeping your right arm straight.
Swinging your leg: Now take your left leg and swing it under your body so that all of your weight is now on your left knee. This should be quick and when you are done you should be in a lunge position. Right arm still straight and eyes still on the prize.
Stand up: From the kneeling position stand straight up while maintaining the weight/eyes overhead.
All four of these steps are just 1/2 the movement. Simply reverse it to end up flat on your back again. Once in the starting position you have completed one rep. Of course you will have to switch sides so the weight is in your left and you support yourself on your right elbow/hand knee. You can see how this works your entire body.
How do you incorporate them in your training? Realistically they can be done at any time but I think they are great both as warmups and finishers. Initially I'd suggest starting out with little or no weight until you feel you have mastered the movement. From there I would suggest adding a little weight and doing 1/2 getups or maybe more appropriately 1/4 getups. Simply put the weight above your head and focus on getting the hip roll and transitioning to putting all your weight on your hand. Stop yourself short of getting to the kneeling position and lay down flat again. Again after you feel comfortable then incorporate the full TGU with weight. Start with 5 reps to each side. Ideally once you get it down these are supposed to be done heavy with lower reps not in a fast paced conditioning type of way.
Originally, TGUs are done with a kettlebell (explaining my Soviet reference earlier) but can be done with a dumbbell, barbell or even your wife!!! The rule here is don't bite off more than you can chew. Start slow and build your way up. As with all overhead movements if you get over ambitious and can cause yourself alot of pain. Remember, the goal to any training whether it is resistance, endurance, explosive, balance or whatever is to avoid/prevent injury first and developing strength second.
Good Luck Comrades