Want to gift shares of stock to a non-US students studying in US. What do I need to do? What does the student need to do?
It depend on how they are held.
Paper Stock Certificates
If you have actual paper stock certificates, you can hand them over and complete a stock transfer form.
Securities in a US Brokerage Account
The shares can be transferred by your broker to the recipients' US brokerage account. Most likely they would be transferred through the FOP (free of payment) transfer system. Your broker will be able to help you through this. If the recipients do not have a brokerage account, they would need to set one up. It might be quicker if it is the same brokerage firm, but doesn't have to be.