You'll probably need a wireless printer to print from your android phone to the printer if you don't already have one.
Then you will need an eprint app for your phone to print to your HP printer.
Here's the steps to print things from your android phone to your HP wireless printer.
Open the HP ePrint app, and then tap Photos or Recent Photos.
Select a photo that you want to print, and then tap Preview.
On the preview screen, tap your printer or the No Printers Found button.
On the Printers screen, tap the plus sign