For most cuts you should let the meat rest before carving or serving. Even after resting you will lose juices as you carve so use a cutting board with a well or lip around the edge to contain the juices. Meat is made up of thousands of small strands of muscle and the way you slice it will determine how tender or tough it turns out. Always carve against the grain. This is particular true with tougher cuts such as brisket or flank steak. You should be able to see the grain much like you do in a piece of wood. Carving against or across the grain will make the meat very tender while carving with the grain will make the exact same cut of meat stringy and tough.
Always use a sharp, thin bladed knife and a fork to stabilize the meat. However, avoid puncturing the meat as much as possible as this will release juices. Carve uniform slices at a slight bias or angle as this creates a more attractive presentation when plating and place slices on a large, flat serving platter.
Carving cuts such as boneless roast, loins/tenderloins and brisket is a simple process. Carving whole poultry or other bone-in cuts takes a bit more practice and is more art than science. For chicken and turkey, remove the drumsticks (they should simply pull off if cooked properly), and slice under the breast and carve off one side of the breast as one large slice. You can then more easily slice this piece into serving portions. For ham or leg of lamb you can slice off a piece to serve as a flat base to help stabilize the cut and then carve individual slices.
Ideally, carve just enough for immediate plating, leaving the rest of the cut intact to remain warm and juicy - you can always come back and carve more if needed.