Okay, here's how it works...
First of all, you need software to un-rar the files. Something like stuffit or winrar. You can download it for free. Just google for software compatible with your system and then install it.
Okay, you need to download ALL of the rar files. You can't unrar them individually. Download all the parts onto your desktop. Then double click on part 1 and let the software do the rest for you. It may take some time, so don't get impatient. You'll see a little counter in a box that shows you the files being opened. If the files have been rar-ed correctly, it should join up all the separate files as it opens them and you'll be left with a single file. You don't need to open each part individually.
If you get a request for a password, that means the person who uploaded the files has protected them. If that's the case, they should have also given you the password to go with the files. Just fill it in the box and press enter. If you don't have the password, you can't open the files.
Problems: sometimes an individual rar file can get corrupted and you'll get an error message. Try downloading the corrupt file again, perhaps from a mirror site (files are frequently available through different servers or 'mirror' sites - you'll see the options at rapidshare). Sometimes the file is corrupted during the upload and will be screwy whatever you do. You have to ask the poster to check the files and, if necessary, upload again.
Another problem: sometimes unrar software is incompatible with the rar software. Not much you can do about this. You'll get a message saying the file can't be opened. Unless you can establish which software was used to upload and use the same software to download, you can't do much about it. But the problem is rare.
Does all that make sense?
Oh yes, just trash all the old rar files after you've opened them. Once they've been opened, you don't need em any more.
If you have any more problems, post again and someone will answer you. We've all been newbies at one time.