The truth is that the answer to that question is both simple and complicated. There’s a way to make a conga at home, but it is extremely laborious and complicated, and it is not worth the trouble. You will need many power tools and expensive materials.
In the end, it will cost a lot more money than buying one from the market. And the result will be lacking in sound quality, and its structure will probably fall apart. Some things are better left for the hands of expert craftsmen who have been doing this all their lives. You could, however, create a high-quality drum throne on your own if you want to.