Step 1 is to understand the exact laws of our universe, back to the big bang. We hope and expect that we will eventually end up with some mathematical equations or structures that are very constraining: Basically, that there will be only one simple self-consistent theory that can possibly be the laws of physics of the universe (or multiverse). Of course, people expect that this theory is string theory: They expect that any plausible self-consistent theory that includes general relativity and QFT is either string theory or something mathematically equivalent to string theory.
Step 2, you extrapolate these laws to learn about unobservable things, including whether there are other universes besides our own. In what we understand of string theory so far, it seems that, yes there have to be many universes, each with different fundamental constants. (Our universe had better be one of the possibilities of course!)
Step 3A, IF it is possible to find a sensible measure of the frequency in which any given type of universe appears: In principle, it is possible to estimate the expected number of intelligent life-forms in each universe. Then by doing a weighted average you can get a probability distribution of what the value of each parameter would be for a randomly-selected intelligent life-form. Then we can see where we fit in this distribution. If we are within a couple standard deviations of the center, good. If we're many standard deviations away, out in the tail, it counts against the likelihood of these laws of physics. I mean, if we have a Bayesian analysis to decide "what are the laws of physics", the finding that our universe is a real outlier among universes with intelligent life would lower our judged likelihood that string theory is the correct one. (Maybe it is still correct, because the other alternatives to string theory, if any, require even more unlikely coincidences.)
Step 3B, IF it is NOT possible to find a sensible measure of the frequency in which any given type of universe appears ("there are infinitely many of each so they don't have a well-defined ratio"): Then the best we can do is show that our universe is one of the possibilities. We will never be able to explain why we are in one mathematically-allowed life-supporting universe rather than another, because there is no explanation.
The overwhelming majority of the "scientific theory" in the anthropic principle comes in steps 1 and 2. Step 3 is a research program to (possibly) get some "predictions" which we can compare to reality, which adds some extra information and falsifiability to the theory. That's all good, but still, there is vastly more information and falsifiability in step 1 than in step 3. That's why, since Step 1 is still very far from complete, people's time is by and large better spent working on Step 1 rather than Step 3.