Ok, this is a pretty commonly asked question, seeing as 90% of the people ripping DVD's aren't doing so because they want to pay money. Since I havn't been able to find a concise and simple guide to this, I thought I would write my own short howto.
Step 1 - Get the software:
You will need 2 program to make this work, DVD Decrypter (which can be found here), and Auto Gordian Knot (known as Auto GK for short, and it can be found here). Download and install these 2 programs before beginning.
Step 2 - Decrypt the DVD:
Almost all DVD's are now shipped as encrypted, lucky for us, DVD Decrypter does just what its name says, it decrypts dvds. Open DVD Decrypter, and select the drive with your DVD in it, then select a target folder and start the rip. Once this completes (It should not take too long, but still, you shouldn't panic if it takes a couple of minutes) close DVD Decrypter.
Step 3 - Encode Video:
This last step takes the longest and is the hardest, but lucky for us Auto GK makes the process relatively painless. Fire up Auto GK, and select and input and an output file, the input file should be one of the decrypted .VOB's from your run of DVD Decryptor. You can select any encoding settings you want, although the standard for a full length film is generally one Video CD and Divx or Xvid encoding. This step may take several hours depending on the speed of your computer, but once it is done, you can delete the decrypted .VOB's and use your new DVD rip!