Try looking on the box, or check your emails sent from Adobe, and the serial number should appear there. If not, ring support, and give full details of the order, and they will send you the serial number again.
If, however you have an illegal version of adobe, or a trial version of adobe, it is against all laws, both national and international, to get a serial number for adobe, unless you have purchased the product (try looking on Amazon for some good deals for adobe)
Either through the application under the Help menu at "Activation," or by contacting adobe to retrieve yours serial, or purchase one if this is the first time activating your product. However, due to the fact that this is very old software, Adobe may no longer support it, meaning they may not be able to provide a serial for you anymore.
Copy and paste "Find a serial number - Adobe" into your search engine and hit enter on your keyboard. Click on the "Find a serial number - Adobe" link in the search results, it will take you to an Adobe support page that will help you get your serial number.
You can only buy the serial number for Adobe Photoshop from Microsoft or just download its crack.