If a state had some land that contained natural resources or strategic interest but lost it to another entity that isn't based in the country or owned by the state, how would they go about recovering that land? I already understand that buying is the best option, but what would a state or leader to if the owners did not want to sell? I heard about nationalization, but it doesn't explain how the land can be recovered. Thanks.
A state can seize any real estate within its borders through eminent domain. The legal framework for this varies from country to country. But almost every state in the world has laws which allow the government to do that if they consider it necessary for the well-being of the population. Sometimes the owners are entitled to a fair compensation, sometimes there are ways to prevent it legally. Details depend on the country.
When the owner is a business from another country, then there might be a trade agreement which guarantees investment protection to foreign investors. In that case, the business might be able to sue the seizing government in an international court or arbitration tribunal and receive compensation not just for the real estate but also for any lost profits.
How could this happen?
One scenario is a region of land is sold (in a normal transaction) to a foreign owner. In this case the land remains part of the country (law of the country apply there and so on.)
In this case the land hasn't really been lost. It is possible for the country to create a law that says "This area of land is now owned by the government". This kind of nationalisation has occurred from time to time, for example in Zimbabwe. Such a law can be passed by the country's parliament, or willed by the dictator, according to who is in control of the country.
If the foreign owner doesn't want to hand over the land, the the country's police and army can go and enforce the law.
This is usually a "bad idea" because in the future other foreign countries will refuse to invest in the country and the effect of this kind of nationalisation is to damage the country's reputation and ultimately the country's economy.
A second kind of nationalisation is the country passes a law which says "This land now belongs to the country, and we will pay $xxx for it. If the amount of money is seen as "fair" this can be done without serious damage to the country's reputation.
It is more likely that most mature nations would simply purchase back the land. The "fair" price is the price that the seller is willing to accept and the buyer is willing to spend. And if a companies only care about "a fair price". If a company doesn't want to sell, that simply means that your offer is too low.
An alternative scenario is that the region of land has not only been bought by a foreign power, but occupied by a military force. In which case it doesn't matter how many laws the country creates, the only way to regain it is by military action, ie war.
A Chinese owned mining company in South Africa. If the government of SA wanted, it could nationalise the mine, taking ownership of it. This is because the mine remains in SA and under SA law. The Chinese company doesn't have the resources to prevent this. But if SA did this without making reasonable payment, then Chinese (and other) investment in SA would drop, making SA poorer.
The Golan heights are occupied by Israel. There are effectively controlled by Israel. If Syria wanted to regain control, it would have to do so militarily, as it doesn't have de-facto control of the region.