I make my tip overlays about 1 3/4" long......3/4" below the string nock and 1" above. Taper the tip area as shown in the image below.
I cut my tip overlays with my band saw and do some preliminary shaping with a disc sander. You can certainly do it with a hand saw and rasp if needed. Make sure the cut on your bow tip and the overlay are absolutely flat and mate up well. Next you're ready to glue the overlay material on. I usually use Titebond II or III.
Once the glue has cured well, you can start shaping the tip. I use a drum sander, rasp and cabinet scraper. The string nock is cut with a round file........small chain saw files work very well. I start in the grove already established in the bow tip from the tillering process. This process will take a little practice.....perhaps on some scrap wood.
My tips are usually about 3/8" to 7/16" wide at the string nock. Hope this helps. Good luck and have fun!