I would however like to know what you mean by "install itself"
By having your printer plugged into the computer, booting it, and after 30 seconds or so, turning on the printer. Sometimes, one will simply find the drivers on it's own & self install. Others, and I don't have a snapshot, so can't provide one, you go into Administration > Printers & from there, add yours. You'll have to be a little self reliant here, so if it doesn't self install, go to where I just pointed in the last sentence, and see if any printers are showing. If so, make it default, if it's the one you mention.
There's a driver list in the 'Add' function, though to possibly save some steps, be sure to check your Driver Manager first. Anyway, on that driver list, you just choose your make, then model, of printer & it may it may not offer drivers. Keep in mind, the newer the printer, the better, just as wireless & graphics cards.
Plus there are some .deb installer files for some printers (though you must search for these), which makes the whole deal a breeze, however this isn't the norm, nor do I know how to convert .exe files into .deb ones, other than I've read it's a long & tiring process that may or may not produce the desired effect. And note, as you likely already know, that all of the functions of a printer designed for Windows won't do so on a Linux OS. You'll be able to have print & scan management, and possibly Fax, if it has that function.
Speciality effects such as correcting skin tone, removal of red eyes or color restoration with photos, forget it. Any of this has to be done with Linux software designed for the job. I doubt that even HP extends all of these apps to Linux users.
I have the driver downloaded and checked the md5sum at the official Dell site.
If this isn't a native Linux file, you're going to run into troubles. As I stated prior, conversion of .exe to .deb files is difficult & not an exact science. In a perfect world, it would be, installing everything with a single .deb file & having all of the native functions (& bloat) that comes with the printers, that up to (on some models) a 300MiB .exe file is required.
I'm a Linux user, not really a student steadily wanting to learn every trick in the book, so I cannot provide answers as to file conversion questions. When I need to learn something for my own use, I'll research & if can't find an answer, will ask here. Other than that, I just run the OS as is after it's setup the way I like it.
Though I still also have an open Topic of my own in regards to printing, the way it's looking, will address it when it's time for a new printer, with a true wireless one. Seems like no one has an answer for sharing a USB printer over a share port on the back of a Linksys router designed for that purpose on Windows & Mac, have tried many things to no avail. Yet I can fire up a Windows 7 VM that's installed inside of Mint's /home partition & print like mad. I don't 'get it', everything that travels to these VM's does so through the OS it's installed on.
Even my Bluetooth 4.0 connection, which is part of my wireless card, shows on VMware Player VM's if enabled, yet doesn't on Linux Mint, though there's likely software in the Package Manager to make it work & be displayed. I suppose that's the 'point to point' device that shows as not configured in the Network settings. That's not an issue for me, as I have it disabled anyway on Windows, an open BT connection could be an invitation to intrusion. Unlike the wireless card's connection, BT signal doesn't go through the router's Firewall, which I have fairly well secured. A device can simply pair to it, if the one on the other end knows what to do to mate it.
Let us know when you get that printer configured & the steps that were needed, it may assist others.