The most important consideration is matching the two pieces as possible. Having done that, the next step is to decide how to glue them together. One suggestion already mentioned is to use hide glue or thickened and tinted epoxy without dowel firstname.lastname@example.org, which, I agree, is sufficient, since it is only decorative. The advantage of the hide glue over epoxy is that it can be reset with hot water or steam. Epoxy is like steel. It works best with little clapping. It is gap filling. That's where the thickening comes in. In either case, you have set up clamps or a jig to hold the pieces while the glue dries/cures. Be sure to wipe all the excess glue off before it sets. Epoxy is forever. You want to preserve the finish as much as possible. Sanding opens up a can of worms. Using a dowel is a lot more work leaving you with the same problem of aligning the pieces. In most similar situations, I would drill oversized holes, mix up a batch of thickened and tinted epoxy and put the pieces together as discussed. Yes, it is a lot of fastidious work.