A decent file archiver, compresses and extracts a variety of archive and file types!
Probably, you need to download the .exe file for the 32-bit system. The size of the installation file is lower than 1 MB, so downloading should be pretty fast.
Now there should be downloaded the installation file with the name 7zXXX.exe on your desktop (where XXX is number of the current version). If you downloaded it to any other folder, just find it with Windows Explorer. Do you have it? Ok. Now double click on that file. Installation will start. As the first step of the installation you can Choose Install Location.

Pre-selected folder is ok in most cases. So click on Install and the installation will proceed. Then click on Finish. 7-Zip is installed now. It's pretty easy, isn't it?
If everything went fine with the installation, you have the new program group in the menu Start > Programs > 7-Zip. Go there and click on 7-Zip File Manager. The 7-Zip utility will start for the first time! You can see its basic window.

It's a good practice to have associated a particular file type with a particular application which can handle this file. For setting up of these associations for 7-Zip files run 7-Zip (Start > Programs > 7-Zip > 7-Zip File Manager) and then click on Tools > Options.

New Options window appears. On the first tab, called System, you can associate 7-Zip utility with a several file types. We recommend to associate all file types by clicking on "Select all" button and then OK button. You can look at other settings too.

Now you have associated all the files which 7-Zip can handle. And finally, 7-Zip is succesfully installed.
It's done! Congratulations!