To test the effectiveness of a new supplement, one group is given the supplement, and the other group is not given anything. Which is the most complete

This would be what is called a regular experiment. Because one group is given the active substance and the other group is not given anything, we can see the difference that happens on a certain variable that is of interest to us following the use of this supplement. Usually it's better to have a double blind placebo-controlled randomized trial, where the group who doesn't receive 'anything' actually doesn't know it's not receiving anything.