I see in my own situation I do not work on doing God's will. I rather have found a kind of comfort zone. But now I realize I could do a lot more, and a lot better if I really wanted to.
What would that entail? I am not sure. I can see that given the right situation and emphasis I can learn Torah, Physics and Metaphysics as per the course study that the Rambam [Maimonides] prescribed. But I clearly am not in such a situation, and I also do not know in practical vein how to in fact turn my will to God's will.
How do you know what good character is?  You go by prima facie the way things seem before you apply reasons. Then if there is overwhelming evidence your original assumption is wrong, then you change it. But morality is not a subject that is so hard to figure out. We know it is not right to torture people for the fun of it, that we should pay our bills, we should be compassionate and honest in our dealings with all people. It would take a lot of evidence to overturn these beliefs. And, in fact, no evidence can ever be brought against them-- since you can not derive an "ought" from an "is."
Philosophers usually make it their business to make up nice sounding principles that would imply the negative of the above mentioned moral principles. Marx for example decided "All property is theft," and thus that would imply it is OK to steal. But think how the logic works. If you have a principle A by which B is implied, but B is counter intuitive. Then you have to see if "A" is more likely or "not B." If "not B" is more clear than "A," then "A" must be discarded.
But outside of basic principles, it is often impossible to tell what God's will really is even if one is sincerely interested in doing it. I have had that problem for as long as I remember. [I could perhaps go into some of the issues but mainly my feeling is that since God's will is so hidden, the best thing I suggest is to learn Musar [books of Ethics from the Middle Ages like the Obligations of the Heart by Rabbainu Bechayee Ben Pakuda.]
The main thing I liked about that book on Spectral theory was the first four chapters but also the clarity it brings to how eigenvalues help solve PDEs. What I mean is if you are into Quantum Mechanics you should see that book. It is a real eye opener.