It sounds like you have the trial for AnyDVD installed on your computer. That is a good start. You can use it to break encryption on commercial dvds. Just let it run in the background....you'll see a fox icon at the bottom right of the screen.
You can also use it to rip to the hard drive. Right click on the fox icon and you will see an option to Rip DVD Video to Harddisk. This will put the entire dvd onto your hard drive in the area you designate. Many newer dvds will need to be handled this way, since they have some nasty protection schemes that interfere with ripping and working with the files.
It is also possible to use other ripping programs and let AnyDVD do the hard part of decryption....this works most of the time, but not on all the very newest releases.
Many dvds are too large to burn to a single layer dvd. You should get a free compression program called DVDShrink. Click on the DVDShrink link in the previous sentence and you'll go to the download page here at cdfreaks. Look through the guides for Shrink here in the Copy Movie forum, or go to www.mrbass.org and read his guides for using Shrink for compression.
You can burn the result from DVDShrink with any program capable of burning dvd-video. I use ImgBurn, which is free. Look at the ImgBurn forums for guides on using it if you are interested.