With your finger slightly bent, starting halfway between the first two joints, run a 1/4" wide strip of tape vertically, around the tip, and back down the same distance on the other side of your finger.  Make sure this vertical strip covers your split.

Again using a 1/4" wide strip, starting at the fingertip and working toward the hand, wrap down to just above the first joint, making sure to overlap the wraps by at least a third.  Because your fingertip tapers, you'll notice that it's impossible to keep the slack out of the wraps all the way around.  That's okay, just make sure to keep the wraps smooth and evenly tensioned on the front side.  Let any slack build up on the fingernail side.

Anchor the tape job by making a figure 8 wrap around the joint.  Do this with your finger bent.  The wrap will pass on either side of the knuckle on the back of your finger and cross on the inside of the joint.

Follow the figure 8 with a single wrap around your finger.

Finish by pinching the slack out of the fingernail side of the wraps from step #2.  Your tape job will stretch out during the first few pitches so it should feel a little too tight at first, without cutting off your circulation.