How can we find contentment and peace according to Taoism?
Serious, if you really read Lao Tzu in earnest.. you'll find that being useless is the key to contentment. The uncarved block, neither especially smart, or especially dumb, not thinking too much, or too little. Just doing whatever is enjoyable at the time.
Thanks for the very good question, I'll try to answer it.
First of all Taoism has a long history, as part of its history it has developed different tools just for this. This means that there isn't a single answer that every taoist group will tell you. But there are some basic principles that you can find pretty much everywhere in Taoism.
Of course reading Lao Tzu would be good, but you really have no clue if what you read, and what you understand is really what the author meant. For this you really need to find someone who gives you a transmission of it, and people like this simply aren't very commonly available. But it is a good read, it is inspiring, and you might get something out of that. Once you are there you should probably also read Chuang Tzu and The I Ching. The I Ching in particular is more the Taoist manual on what to do when the situation is such and such. Don't 'throw the coins'. Read it. As if it was a book, one situation after the other.
But then there is something else. One thing that pretty much all of taoist agree on is that to develop health is a good thing to start from the body. Remember that taoist see emotional and mental well being as states of health. So you want to develop this emotional and mental health. The fact is that many mental and emotional unpleasant states can sometimes be tied with problem in the body. Example, you eat badly, your liver gets clogged, and then you are angry. You might be under the illusion that the problem is that this person did this or that, but actually the problem is in what you eat. SO Taoists tend to pay attention to their body. And here you have all the practices to heal the body, the Qi Gung, the Tai Qi, but also the Taoist 5 elements diet, but also all the Chinese medicine fits here. You can see how this is a big topic. But once you have a reasonably mastered it, you will have probably reached an acceptable level of well being. Much better than before.
But then you might realise that you happiness, your well being, your contentment is still far from complete. And now you might have reached a second obstacle. Let's imagine there was something in your life that happened. Something that is bothering you. What could that be? You are a guy, a classic would be being bullied as a kid. For women rape is a big one (for men too, but the data are less around). But there are many others. Seeing someone die. Another common, being beaten by your parents. In short, take a shock, any shock. And every human being have had plenty of shocks in their lifetime.
Some of those just go, but some don't. The ones that don't can sometimes remain with us for a lifetime, and truly robs us of the joy of being alive. No amount of Qi Gung will help you there. No diet can recover you from them. For that you need meditation. So in taoism you are not considered to be a truly grown person until you have gone over all your childhood traumas. And you will not be truly content and happy until you have let go of all of that baggage. So for that you need meditation, and there are specific techniques, and different taoist groups teach different techniques. And so on.
And then you in taoism you have all this jazz about being in tune with nature, and being spontaneous.
Another thing you need to consider is that Taoism is generally not a tradition of defeatist. That is (sorry for the spelling) of people who surrender and give up desire. Although Taoism flirted with Buddism for over 1000 years, in general the taoist point of view is to develop your destiny (your ming), and only then let it go. If you have inside you to be a music composer then be a music composer, if you have inside you to be ateacher, be a teacher. Even if you have inside yourself to be a great general, be a great general. In short develop the seeds that are inside you, and then you can more easily let them go. And this is also important in the path to contentment. The idea of being yourself fully, embodying your nature, and then let it go.
If you develop your destiny, keep your body healthy, release your emotional and mental blockages, and live in touch with nature (both inside and outside you), how could contentment and peace defy you?