HP Print and Scan Doctor is a free tool for Windows to help resolve common. Install HP Print and Scan Doctor on the computer connected to your printer.
As banhien has noted, there are no drivers to be installed on an Android device. However, it does not look like your printer is supported for printing from Android using the HP ePrint app based on the following link. The simplest method to print would be to get a printer that support the ePrint app or ePrint (printing through the printer's assigned e-mail address) such as the Photosmart 7520, Officejet 8600, etc. Otherwise, you will need to use Google's Cloud print. All information regarding Google Cloud print can be found at the following link. Since your printer is not a cloud ready printer, you will need the steps for a classic printer.