Try to do this but please make sure that you are using a Windows OS or Mac OS.
Since you do not have the installation disc of your printer, you can download the Full Feature Installation software from the HP's website, that's www.hp.com. On the upper right hand of the page, please look for the search field and type in the Product number or the model of your printer, click on the search button or the magnifying glass icon, now, once that the website have searched for the appropriate information, please click on the HP Deskjet 3320 Color Inkjet printer and go to Software & Driver Downloads. It will ask for the operating system of your computer, after selecting your operating system please click on next and go to step 2 (select a download), now, click on Driver - Product Installation Software (2) and select the HP Deskjet Full Feature Software and Driver and then click on Download, It will be downloaded to your computer, After downloading, please search for the downloaded file and run it. That's it! just follow the Installation wizard for you to install the printer to your computer.