Splicing is easy; draw your pattern on piece of paper, cut it out and glue it on your stave with white Elmer's lining up the pattern with a drawn center line on the billet, flatten the belly of your billet so it will run true through the bandsaw. I always have to add a handle piece after I flatten the belly for cutting the splice but that is no problem.
I place my flattened billet on the bandsaw table and sight down it to see if I have the flattened belly cut so the billet will not be twisted on the glue-up. If I am trying to glue up to remove twist I look for the best position to accomplish this.
Cut just outside your lines and fit things together. Unless the stars are aligned you probably won't have a perfect fit. Hold your splice up to a light and look at where the impingement points are that are keeping it from sliding together and sand or file a little until everything fits, then glue up with three clamps. I put one clamp on the middle of the splice and adjust the billet center lines so they line up then finish clamping.
I am replacing a bad limb in this picture.
Here is the finished repair with the added handle piece. The initial bow was made from spliced billets, the darker wood is from the earlier splice.