So an example on a Macintosh. Put in the DVD and run Mac the Ripper which is a free program. Leave the controls as they are and it will copy the entire DVD. Or segment the DVD and just copy the movie or parts of the DVD that you want. Either way, after indicating where the copy should go to - just start 'er up and in a little while it's finished. The Video-TS folder that results can now be filed into a special folder for DVDs if you like or placed wherever you want. To watch it, just launch the Apple DVD player and have it select a Media File to play - which in this case will be the Video_TS folder. Hit the play button on the DVD program and proceed as normal. To store just the movie, running a program like Turbo.264 HD will let you toss away all but the movie and then save it in a format for easy viewing - say those wanting to use their AppleTV.
Of course there are other programs available for the Macintosh for ripping DVDs, some costing money and some with more complexity. The basic procedure is simple, as you can see, and one that pretty much anyone can do.
It is just as easy for PC users who are looking for a solution for ripping DVDs. A number of programs are available for use that basically do the same thing as on the Apple side. One example being DVDFab Decrypter which not only rips the DVD but can convert it to a format for viewing on other devices if desired (such as a PSP, iPod, etc.).