Indian investors can invest in international markets by trading some of the indices that are traded on NSE, most importantly Dow Jones and S&P 500. This is the safest and the best way to trade foreign stocks or indices.
Some Indian brokers also give clients an option to open an account with them to trade international stocks, but this is not advisable simply because I presume the cost of opening an account will be high and the paperwork will be humongous. If you really want to trade foreign stocks, it’s best for you to go abroad, live there for a while and then get yourself an account opened with a local broker there. This will get you in the right way and you’ll be able to participate like a local would.