There are a number of ways in which this can happen. Most of these involve becoming more productive and/or taking advantage of international trade.
Three of the most important examples of how countries with few resources can become rich are to be found in Asia. Since World War II, Singapore (under Lee Kuan Yew), Japan, and Hong Kong (which is, of course, not exactly a country) have become very wealthy even though none of these countries has a great deal of productive land or other resources.
Countries can become rich by involving themselves in high value-added industries that are not dependent upon the possession of land. For example, Lee Kuan Yew directed Singapore’s development towards things like financial services. Singapore was able to become a center of banking, which requires no productive land. Today, the country is also moving into things like biotechnology which also need an educated and productive population, but not land.
Countries can become rich through industry as well. This has been the Japanese model. Even though the country has few resources, it has been able to import raw materials and make them into high value-added finished products that were mostly exported to other countries.
Land is not the only factor that can make a country rich. The country’s human resources and its willingness to innovate are also very important factors.