There are two ways of investing in a public company that has its headquarters in a foreign company. The simplest way is when the company is listed on a stock exchange within your own company. Frequently these companies have a dual listing meaning that they are listed in the country where they are headquartered and in your own country.
When these dual-listing companies list in the USA they are referred to as ADR listings. Examples of ADR listings are Baidu.com (BIDU), the Chinese-language internet search company with headquarters in Beijing, China, and BHP-Billiton (BHP), the mining company with headquarters in Melbourne, Australia.
In the case of Australia, there are a number of Chinese mining companies that have listed on the Australian Stock Exchange in order to get easier access to Australian capital.
If the company that you are interested in has a dual listing in your own country, then this is the easiest way to invest since the transactions take place in your own currency on an exchange in your own country.
If a company that is headquartered overseas does not have a dual listing in your own country, the first step is to contact your own broker to see if they allow trading on overseas markets. In some cases they may ask you to open a special account. Frequently the transaction costs charged by the broker will be higher.
Another method is to open an account with a broker that specializes in international markets. One such broker is Interactive Brokers: www.interactivebrokers.com.