Start by lightly rubbing saddle soap all over the first base mitt. Use a clean rag and a small amount of saddle soap and rub it on using a circular pattern all over the leather. Extra rubbing won't hurt the glove but too much saddle soap can weaken the leather so use it sparingly. Other options for rubbing include Vaseline, baby oil and baseball glove oil.
Place a baseball into the pocket area of the mitt. This is between the thumb and index finger. Close the glove and tie a string around it to keep it closed and holding the ball. Leave it tied for several days before removing the string. This will help you form a good pocket. Having a properly-formed pocket can help a first baseman greatly when trying to catch low throws from the shortstop or hot smashes down the line.
Once you untie the string and remove the baseball, insert your hand into the glove and open and close it several times. Take a ball and place it into the pocket and close the glove tightly several times. Repeat this process several times a day over a period of a week or so.
Bend the edges of the glove in and out with your hand inside. Remove your hand and roll the edges of the glove in and out several times. Repeat this several times a day over a period of a week or more if necessary.
Place the mitt on the ground and hit it with a baseball bat. Be sure to hit all sides. This will help to break down the leather fibers and make the glove softer. You can also use a ball-peen hammer to accomplish the same task.
Insert your hand into the glove and play catch. The best way to break in a first baseman's mitt is by using it, so the more you play catch the faster it will break in. The combination of the warmth and oils from your hand will help soften the glove and form the pocket.