How do individuals meet their obligations to society (if any)?

Do they do it through voluntary exchange, altruism and compassion.

Or do they do it out of compulsion because they are threatened with violence?

The latter is obviously not what we want, but its the State we have. Reducing the size of the state therefore sounds like a good plan, since it should reduce the amount of threatening with violence that has to be done.

It seems to me that reasoning is backwards. People agree to come together in society because the believe that doing so will allow their needs to be met. If their needs are not being met but they still go along with society, then it is likely because of the threat of violence if they do not.

For example, I recognize someone else's home as private property because I want my own home to be recognized as private property. However, if a society's economy is such that I cannot afford a house then the only motivation for me to respect someone else's home as private property is because society threatens to throw me in jail if I don't.

As I said, the State we have is violent by its nature. I'm suggesting this is not what we want.

You not trespassing on somebody's home because you don't want your own to be treated that way is a great moral to hold, but not shared by everyone. A society can only function like this if people are on the same page - if they share a collective moral framework. Traditionally this was through religion, but these days "god is dead", and large scale immigration has led to societies with no common traditions or moral backgrounds.

In a nation where people have arms, then the most legitimate reason not to trespass in somebody's house is that you don't want to be shot by its owner. The decision to trespass in somebody's home is a choice between your life or whatever you may gain from trespassing. The choice is obvious.

Burglary is quite high in the UK where people don't have arms (or if they do for sport or hunting, they are not allowed to use them for self-defence). It is lower (per capita) in the US.

And self-defence, even if lethal force is used, is never "violence." (A common misunderstanding)

The way individuals should meet their obligations to society is through the non-aggression principle. One should not support any kind of violence, or threat of violence against others. What follows then, is peaceful, voluntary cooperation.

If I don't trespass because I don't want to be shot then that sounds like the homeowner is violating the non-aggression principle. They are using the threat of aggression to motivate me to do what they want.

As I stated above, self-defence is never violence. This includes stating your intent to defend yourself, your family and your property even with lethal force. You shouldn't need to state it though, it should be assumed.

A homeowner cannot possibly know the motive of a trespasser, and it is therefore completely rational for them to use lethal self-defence, because they must assume the worst-case, that the trespasser may harm them or their family.

So there is no violation of the NAP here - the trespasser is the only one who may be in violation.

Obviously, the vast majority of people aren't out to kill. They don't want to harm someone for stepping onto their lawn, nor do they want to clean up a dead body. The use of self-defence is a last-resort if they feel in danger, or if they feel their property is under threat and it's worth more than the perpetrators life.

If the trespasser decides that somebody's property is worth more than their own life (which is the case if they assume the owner may use lethal self-defence), then there should be no expectation of the property owner valuing the life of the perpetrator more than their property. Both parties agree that the property is worth more than the aggressor’s life.