Here is a very simple way to make a solid splice.
Take both limbs, and set them end to end laid out as if they were one bow already.
Overlap them 6 inches. ( 6 is the minimum, 8 is best )
Have the upper limb to the left of the lower with that 6 inch overlap.
Using a straight edge and a sharpie, draw a straight line from the upper corner of one limb to the lower opposite corner of the other.
That is the line that will define your splice. Its just a line that resembles a not equal to symbol. Where the equal symbol are you limbs, the slash is your splice.
If you are good with your basic handsaw, clamp both limbs side by side and cut them both on the line at once. You may want to fashion a miter box of sorts to keep you straight.
After the cut is made, test fit the limbs togeather. Any inconsistancies in the cut can be fixed with a 2x4 clamped to a table with 8 grit on top. Pretend this sanding block is a belt sander, and rub the cut limb over it to fix any uneveness ( that word looks strange ) in your joint. Some gap is ok, but anything over 1/8 inch I would for sure fix. Use a good gap filling glue or epoxy. I use tighbond 3. It has worked for me on bows up to 55 lbs no worries.