I have an object defined as a list of triangle indexes and a list of vertices. I have to generate a tetrahedron mesh from that list. The triangles define a closed surface. I saw there are a lot of papers on algorithms but they are too abstract for me to understand. I saw that there are tools for this kind of operation too but I need to implement it myself so that I can fully understand it. Can someone please tell me a method which isn't too complicated?

I'm going on a lot of assumptions: If you have a convex tesselation and it's Delaunay (is it?), then the vast majority of your job is already done for you. I think that the goal from there is to use those triangles and vertices to make tetrahedra that each have the smallest possible enclosing sphere that contains no vertices other than the 4 that make up the tetrahedron in question (you may need to drop this 4 vertex limit, I'm not entirely sure, try it both ways). So what do you really have, because this is basically too good to be true? In terms of brute force algorithms alone, facing something like an O(n^2) time complexity here (where n is number of vertices, which is also roughly proportional to triangle count 2n - 4 for a convex tesselation), when you really could have been facing something horrific like O(n^4) if you hadn't started with the seed triangles in hand is a pretty gigantic break, so I gotta wonder if it's really what you have.