Can anyone guide me how to purchase things from Amazon and enjoy free shipping to Singapore?

As Idza mentioned, your items have to be $125USD minimum. You'd have to ensure that all items have to be eligible for the AmazonGlobal Program and sold by Amazon.com and total weight less than 20 pounds (9.07kg). Here's a guide that might help: http://www.singaboleh.com/amazon-free-shipping-singapore/