I really like to fillet one side of a large shad. Cut the head off with some meat still attached to it and cut the tail fin off. You should have 3 sweet pieces of shad bait. (Two fillets with the backbone on, the other side, and a bloody head with some meat on it). If the shad was a monster or I am fishing for channels or eaters, I cut the fillets down in more pieces.
If the shad is small, I cut em in two in about the middle and cut the tail fin off because it can get in the way of a hookup. If the shad is smaller than about 4-5 inches, I hook the whole thing on. Sometimes I slice smaller shad in horizontal lines from behind the gills to the tail. I feel like the juices get out better. However, I think the bait fishes faster so it can attract fish faster, but it also water logs faster and I feel I need to change it more often.
One thing I like to do is to scale the shad with the back of my fillet knife before I chop it up.
Hope this helps. Tight lines.
Edit: Almost forgot, hook the shad in a place where you expose a lot of hookpoint and provide a clear path between the hook point and the fish's jawbone. Do not overload the cutbait on the hook. Imho, the deeper you hide the hook, the more fish you will miss.