This is what I did to find the driver necessary to install your printer to a new computer:
1: Visit Lexmark's Driver Download Site
2: In the section that reads, "Download by Product" type in: Z611
3: Click the image/link of your printer (might take a moment to appear above the text-area).
4: Scroll down and find the appropriate driver that corresponds to your Operating System (If you have Windows XP, download the driver for XP. If you have Windows Vista, download the driver for Vista).
If the method above does not work for you, Microsoft has been getting better at locating drivers for you through Microsoft Update. If you're running Windows XP, go to the regular Windows Update page and look for links for Microsoft Update (By default, Microsoft Update is not used for Windows XP. You have to request it through Windows Update). After "signing" an agreement and installing a few more files Microsoft Update will look for updates to your system. Once the results are displayed look into the "Hardware" section. If you find anything in regards to a printer, chances are Microsoft found a compatible driver they know will work for your printer. Remember, before Microsoft Update can locate drivers for your printer it has to be connected to the computer and turned on.
If you're using Vista (W7 is just an enhanced version of Vista, yet Vista nonetheless), just go to your Start Menu and search for Microsoft Update -or- Windows Update. Afterward check for new updates and do the same as mentioned above. Look into the hardware section to see if there are any entries for a printer. If there are, select the update and install it. Remember, before Windows / Microsoft Update can find drivers for your printer it needs to be connected to the computer and turned on.
Personally I would use the drivers from Lexmark, yet I figured I would give you two choices. Let us know how things turn out.