It's easy and this will also allow you to burn yourself backup copies (which is in fact not illegal unless you sell the copies, however breaking a disks RCE and/or copy protectioon can be illgeal depending on where you live) So lets get started...

As a note - there will be an update at some point in the future but for now this is a massively out of date instructable.

Step 1: Get the Download

Now for Ripper programs I personal use super DVD Decrypter because it removes all copy protection, regions and can make ISO's for direct burn to disc...
http://dvddecrypter.org.uk/ - unfortunately the project is down for whatever reasons but here's the mirror site.

for macs you can use Mac the ripper thanks to LasVegas for that little bit of knowledge

Step 2: Now Install Your Software

Simply just double click the .EXE and let the installer do its stuff, won't take long.

Now put a dvd in your disc drive and start your shiny new program, it should pick it up automatically.

Here's the view of mine and it had picked up a dvd I had forgotten was in the drive.

Step 3: Now We Rip...

First of all you need to know what you want to do.

You can rip an ISO file (it's an image of the disc which can be burned on to discs making a copy), for that you'll need a burning program capable of burning ISO files, CDXPburner is a free and rather useful program that can burn ISO files and others aswell as having some tricks of it's own. found here

You can rip the files directly to computer by using file mod and making sure all the files are selected, or you can click in your toolbar and choose to only rip the main video files and conver them with This

You should now have a decent idea of how to rip file using these programs, the video converter is dead simple, file in file out, I would give a better set of options for converters but that was the only free one I could get to download.