So you have your new download on the desktop. Now take a look at what it 'is'
Sims 2 downloads come in many forms.
Zips AKA, Things called 'downloadtitle.zip'.
Zips are archives that contain the actual game-file. You'll need to have Winzip installed for these to work. Double-click them to extract the goodies withing.
Sims2packs AKA, Things called 'downloadtitle.sims2pack'
These are the archives that Maxis made for the game. You can extract these by double-clicking them. They'll automatically install the files to the right folder.
Packages AKA, Things called 'downloadtitle.package'
These babies are what you need. They're the actual download files, and the only ones that will work in The Sims 2. You'll need to put these in your downloads folder.