Here is the thing. Stoicism as it was taught 2000 years ago was extremely bound up in its "providential" and deity focus. Not as unpalatable as some of the more direct monotheistic religions, but depending on your teacher stoicism was still on a scale of pantheism to direct theism. (Marcus was very pantheistic and deemphasized religion, Epictetus was much more vocal about the theistic elements). As a modern reader a lot of ancient philosophy is like that. It has elements that you have to excise. So ancient philosophies are not really plug in play for a modern rationalist.
Basically, I think you have to start by writing things down and learning about the elements of these ancient, and modern, philosophies to see the sort of systems they put in place to deal with every day life events and exceptional events. How should I think about X? And some very obvious patterns will emerge. Some elements of stoicism may be difficult to employ and Stoicism in general is a hard to follow (fully) philosophy. The key point Epictetus had was that very few of us have the ability to follow Stoicism (or any coherent, but challenging) philosophy to its fullest. However, we should still endeavor down this path of "progress". This is why Epictetus has stayed so popular. He didn't advocate perfection of philosophy, merely that you work at it.
Which brings me to my final thought for you to answer your question directly: write it all down. For example, Stoicism has a lot of great elements that resemble modern psychology CBT (Cognitive Behavioral Therapy). So you pull the elements of ancient philosophies that work, you augment it with snippets like this Less Wrong articles various things. And you write your own coherent philosophy of life. And then you work at following it. It is pretty easy to lay down ideals, and pretty hard to stick to them. So you have to work at it, almost every day. You have to work on mindfulness and staying present and ensuring you keep your philosophy in mind in every day situations and exceptional situations. And, and this is where it gets tricky if you have trouble with non-empirical elements, you just have to believe your philosophy works. You have to believe it enough to follow it, even if you can't explain all of it. Science has spent the last 2000+ years catching up to things the ancient greeks found to work.
Much like a running coach can't really tell you WHY, exactly, everything he is having you do is working, it just does. Physiology has slowly been providing more and more detail, in the mean time running coaches have learned through trial and error how to train very efficiently. Some day we will probably have an exact explanation for the mechanisms of physiological improvement. Until then we can use our very good heuristics. I would argue it is the same from psychological perspective. It is close enough. Trust in your system and intuition and work to make it better and progress as a human being. There is no "perfect system" for everyone, but I think we could all agree on some pretty broad ideals that count as forward progress as humans :)
Basically, I think you have to start by writing things down and learning about the elements of these ancient, and modern, philosophies to see the sort of systems they put in place to deal with every day life events and exceptional events. How should I think about X? And some very obvious patterns will emerge. Some elements of stoicism may be difficult to employ and Stoicism in general is a hard to follow (fully) philosophy. The key point Epictetus had was that very few of us have the ability to follow Stoicism (or any coherent, but challenging) philosophy to its fullest. However, we should still endeavor down this path of "progress". This is why Epictetus has stayed so popular. He didn't advocate perfection of philosophy, merely that you work at it.
Which brings me to my final thought for you to answer your question directly: write it all down. For example, Stoicism has a lot of great elements that resemble modern psychology CBT (Cognitive Behavioral Therapy). So you pull the elements of ancient philosophies that work, you augment it with snippets like this Less Wrong articles various things. And you write your own coherent philosophy of life. And then you work at following it. It is pretty easy to lay down ideals, and pretty hard to stick to them. So you have to work at it, almost every day. You have to work on mindfulness and staying present and ensuring you keep your philosophy in mind in every day situations and exceptional situations. And, and this is where it gets tricky if you have trouble with non-empirical elements, you just have to believe your philosophy works. You have to believe it enough to follow it, even if you can't explain all of it. Science has spent the last 2000+ years catching up to things the ancient greeks found to work.
Much like a running coach can't really tell you WHY, exactly, everything he is having you do is working, it just does. Physiology has slowly been providing more and more detail, in the mean time running coaches have learned through trial and error how to train very efficiently. Some day we will probably have an exact explanation for the mechanisms of physiological improvement. Until then we can use our very good heuristics. I would argue it is the same from psychological perspective. It is close enough. Trust in your system and intuition and work to make it better and progress as a human being. There is no "perfect system" for everyone, but I think we could all agree on some pretty broad ideals that count as forward progress as humans :)