When it comes to meat, there are 3 criteria to focus on: flavor, tenderness, and juiciness. Flavor is a product of seasonings and the drawing out the inherent flavor of the meat. Tenderness is achieved by cooking long enough to break down the tough connective tissue or preventing overcooking. Even if the meat is tender and flavorful, if it is dry and chalky, then it’s not that exciting.
The number one preventable thing is to not overcook the meat. For beef, cook it until it is just pink with a little brown (internal temp of about 135F). Chicken needs to be cooked to 165F. When it overcooks, the fibers shrink and its ability to hold water is lost.
One technique is to brine meat before cooking. The salt solution causes the meat to absorb some liquid. More liquid to start with hopefully leads to more liquid in the end product.
Another crucial tip is to allow meat to rest. The fibers rearrange themselves when hot and liquid is squeezed out, usually towards the center. When the meat cools, it regains some ability to absorb liquid and it gets reincorporated into the fibers. Think of it this way: you throw a sponge into a wet bucket and then onto a tray. As it “cooks”, you press lightly on the top of it. Water drips out and makes a small puddle near the sponge. You can cut it right there on the spot, but it will be a little dry. If you release your hand from the sponge, it recoils and reabsorbs some of the liquid it lost as it “cools” When you slice it after, it retains more juice.
When you make a steak, take it off the grill and place a foil “tent” (or blanket) over it and allow it to cool for about 10-15 minutes before serving. This means you will have to factor that into the schedule. You will have to allow a roast to rest a little longer than a steak due to its larger size. Another tip is to allow it to rest in its own juice rather than alone on a cutting board. It can soak up liquid from outside as it rests.
In addition, keeping it covered keeps the steam from escaping, preventing it from drying.
There’s tons of scientific reasoning why this works, but in practice, it really does make a difference when you allow meat to rest. Keep it warm however, you don’t want to serve cold meat. A foil tent, or placing it in a cooler would help keep it warm and moist.