I will be happy to assist you with your question. Fisrt off, I would like to explain what WPS is. WPS stands for Wireless Protected Setup and is a method to connect your printer to your router using a push of a button.
The WPS button that you are hearing about is on your router if it is a WPS supported router. There is no WPS button on the PIXMA MX439 so all you need to do is check on your wireless router for a WPS button. If you do not see one, then you would need to perform the wireless setup manually using a USB cable. What this does is allow your printer to download the network settings through the USB cable. So that I can provide specific instructions to perform these steps, please reply with the operating system installed on your computer.
I look forward to assisting you with your PIXMA MX439.
Unfortunately no, you will need a router to be able to print wirelessly from your phone as well. The printer does not support ad hoc network connections which are from the printer to a device. How it works with your phone is that you connect your phone to your local wireless network, then print to your printer which is also connected to this local wireless network.