You'll have different techniques for different recipes. The most important thing is not to overcook it ... but with ground meat and ground poultry in particulary, you want to make sure you've cooked it long enough to be safe.
For amalgameats, like meatloaf and meatballs, the common technique is a panade, breadcrumbs soaked in milk, and adding vegetables helps too (cooked spinich, onions, bell peppers, carrots, etc.)
For sausages, apples are a fairly common item in chicken sausages to add moisture. I don't know that the flavor combination would go as well with beef or pork sausages, but you generally want fattier cuts for sausage anyway.
For burgers, it's even trickier, as if you add a ton of stuff into the burger it becomes something that's more a meatloaf patty than a burger. You can make two thin patties, and put butter or cheese between them, and cook it as a 'stuffed burger', but if you're selecting leaner meats, I'm guessing you won't want to add more back in. Your better option is to cook the burgers in a low oven until they reach your desired internal temperature, then give them a quick sear to develop a crust; this will help minimize the amount of overcooked exterior.