Companies save costs by operating internationally in many ways. Probably the first thing most people think of in answer to this question is that the cost of labor in other countries is often significantly lower than it is, for example, in the United States. Developing countries, first, have much more relaxed laws about things like minimum wage, working conditions, hours, and ages of workers. In addition to this, many countries internationally have an abundance of labor (or people willing to work). This kind of competition means people are willing to work for lower wages.
Another way that companies save money is through a reduced cost in materials when operating internationally. The lower cost of labor in a country affects everything economically. A counter-top manufacturer in the United States, for example, might export all of its granite from a country like India, where the operation costs are significantly lower than many other countries who mine granite, therefore, the price of the granite itself is lower.
Finally, many companies who expand their business internationally save costs in transportation. The cost of shipping something from India to China is going to be lower than the cost of shipping from the US to China.