Choose a brokerage firm or bank that is able to execute orders for you to buy stock on the Swiss Exchange. Most major US brokerage firms can trade on the Swiss Exchange through a Swiss bank. Another option is to open a brokerage account directly with a Swiss brokerage firm or bank. Some online discount brokers also can place buy and sell orders on the Swiss Exchange.
Familiarize yourself with the rules and costs of buying Swiss stocks. Switzerland has liberal regulations for foreign investment, but you should check on your liability for paying Swiss taxes in addition to US taxes on any profits you may realize. Any purchase of foreign stock must be made in that country's currency. This means you will have to pay an additional fee to exchange US dollars for Swiss francs.
Learn the basics of foreign currency exchange and how it affects buying stock on the Swiss Exchange. When the Swiss franc is "strong" against the dollar, Swiss stocks are relatively more expensive. The reason this is important is that if the dollar strengthens while you hold a Swiss stock, the change in currency rates will cause you to receive fewer dollars for the Swiss francs---and this can turn a paper profit from stock appreciation into a net loss. To monitor the exchange rate, go to any foreign exchange website and look for the US dollar/Swiss franc rate. This will be listed as USD/CHF, followed by the exchange rate, which tells you how many Swiss francs it takes to buy one US dollar.
Execute your order via your brokerage or bank trading account. This is a much simpler process than it once was. Your broker needs only to enter your buy order using the SIX Swiss Exchange trading platform, and your trade is normally executed in seconds. As with other exchanges, you can place limit orders, buy on margin, and do all the other types of transactions you are used to.