In IE 6 or 7 go to Tools > Internet Options > Security tab - click on Internet and then on Default level which should be Medium for IE 6 and Medium-High for IE 7. Thee are the basic settings and you should have no problem downloading files.
Putting the sites you want to download from into the Trusted Zone - temporarily- should allow you to download without needing to adjust your securuty settings for that zone. However this does not always work as the download may be hosted on a different site in which case you need to enable ActiveX controls and plugins in the Internet zone. File downloads are enabled by default.
Judy, it is possible your firewall (or other security-related software) is blocking downloads (especially if you cannot download with IE either).
If you cannot download from the same sites with IE either, then please let us know what firewall you are using (if you're using a 3rd party firewall) and any other security-related software you have installed.
Additionally, it may be helpful for us to know what web site(s) you have trouble downloading from (and an example or two of files you cannot download).