Having a bank account in Switzerland (in Swiss Bank) is definitely prestigious. Before going further, I am sure you would want to pick a top bank in Switzerland for the highest level of security. And you would want maximum secrecy. In this case, two of the top banks you can go with are UBS and Credit Suisse Group (which are in Switzerland). And the bank account type you should pick is Numbered Account. Such bank account includes complete interactions with the customers in numbers; no names are involved. (It’s difficult to open numbered accounts though and it requires an initial deposit of at least $100,000. But this is a different topic altogether!)
Coming to your exact question, opening a Swiss bank account is fairly simple for Indians. You submit the form along with other required documents pertaining to your identity (including passport). The bank will do a background check on you with whatever capacity it has. If it finds that you are breaking or trying to break any Swiss regulations, your application will be rejected.
Remember, while these banks in Switzerland are popular to store your black money, these people have strict money laundering laws guarding their operations. So when submitting their applications, you must be extremely careful. Follow their guidelines devotedly. If everything goes well, you can have your account ready in as less as 2 weeks.
However, all being said, there are many watchful laws not just in Switzerland but also in India that prevents from depositing in international banks. Opening a bank account in institutes outside the country in Switzerland is not illegal. You just have to mention about this in your tax filing. But you are advised to let a professional do this for you. You don’t want to overstep FEMA and Anti-Money Laundering laws. It could call in for strict punishment for you. A professional can help you open Swiss bank account in Switzerland much swiftly.