HP will auto-detect your OS, but you can manually change it. For the HP Deskjet 1510, the most common options are:
This is the recommended package, containing the driver and additional tools like the HP Scan software. drivers hp deskjet 1510
You do not need a traditional driver. Install from the App Store or Google Play. Connect your phone to the same Wi-Fi network as the printer (if wireless) or use a USB-OTG cable. HP will auto-detect your OS, but you can manually change it