Before whitening, your dentist would need to perform a basic examination to make sure your teeth and gums are healthy before whitening can be safely prescribed.
The whitening process itself, can cost anything from $800-$2000 depending which clinic you attend and which brand of whitening the clinic offers.
From my own experience, Philips Zoom! is commonly used and the procedure usually takes up to 1hour. The whitening effects can be seen immediately.
Another alternative would be to ask your dentist for custom made whitening trays and a take home whitening kit. Your kit will consist of whitening gel which your dentist will explain how to use. Usually this method of whitening will require you to wear the trays and gel for a specified amount of time, over a 2 week period. This method is more cost effective, with an average range from $300-$700.
Definitely do not attempt to whiten your teeth with anything other than products sold at a Dental Clinic as they will not work, or can cause irreversible damage! If you're unsure, always check with your dentist first. Hope this helps!