When two or more nations engage in free trade how is the standard living improved in the participating countries

The standard of living is improved through something called "comparative advantages", which means that, relative to the nations' total output and ability to make other things, each nation produces something that they're better at making than the other. When the nations trade, they are able to use these comparative advantages to create a more efficient, productive economy.

Even if one nation is wealthier or better off than the other, this principle means that both countries can still become better off through trade.