Insert the chuck key into one of the three holes in the chuck so that its teeth fit inside the grooves of the chuck. Turn the key to the left to loosen the chuck. Once the chuck is loose you can use you hands to finish the job. Hold the bit with one hand on the shank end so that you can stop the bit from falling (and getting damaged).
Step 2: Insert the new bit.
Insert the bit you want you to use into the spindle. Get as much of the shank in there as possible without covering the flutes of the drill bit with the jaws of the chuck. Tighten the chuck by hand first so the bit won't fall to the ground. Place the chuck key in one of the holes and tighten. Tighten the chuck from the other holes as well and that's it. You're ready to drill some holes.