It depends.
Since this is the spreadsheet forum, I'm assuming you're tlaking about Excel.
Autosave is one of the (many) most annoying, yet helpful (?) features of the M$ line of software. In Office 2000, probably in response to so many peopley being ticked off about autosave being "on" by default, made it an "Add-In" in the latest version. Now, to turn Autosave on you have to install the Autosave Add-in (Tools > Add-Ins > check the one(s) you want). Once it's installed, you can turn it off. In your case, you may have an earlier version of Excel and that means you have to find the Autosave check box somewhere in the Tools > Options OR the Edit > Preferences menu/dialogue. It's there.
BTW: if you want those annoying "office assistants" to stop showing up, find the folder named "Actors" and rename it "DeadActors."