Yes, Indian citizens can buy shares of foreign companies, And become the shareholder of some of the most successful companies all over the world.

The actual trading of stocks is done by a licensed foreign broker, but you need a local broker who will coordinate this for you. The local broker will ask you to submit the documents such as Photo id proof, Address Proof and Photograph under latest KYC guidelines. You also need to mention the currency in which you want to settle your transactions. In order to remit funds to the bank account as requested by the foreign broker, you need fill out Form A2 available with your bank. This is all you required to start trading in the foreign companies.

One needs to have a good knowledge of the companies, countries they are listed in, exchange rate fluctuations and the tax treatment on gains of such tradings as the gains are not treated as Long term capital gains the way they are treated in case of domestic companies.