Welcome to the forums shanenation.
Since you don't mention any other programs, I assume you are using the built in ripper in AnyDVD to get the movie onto the hard drive. You should do this in file mode (right click on the fox icon at the bottom right and hit Rip Video DVD to Harddisk). This will put the entire movie onto the hard drive.
Most commercial dvds are too large to fit onto a single layer dvd without compression. You can remove sections you don't want, like foreign audio or directors comments, but many will still need compression. To do that you can use DVDShrink. It is free to download and use (just click on DVDShrink in this paragraph and it will take you to the download here at cdfreaks). Read a few guides for using Shrink at www.mrbass.org or www.dvdshrink.info or here in our Movie Copy Software forum.
You can also use Shrink to do the ripping to the hard drive if you prefer. Just run AnyDVD in the background, and do the ripping from within DVDShrink. This will allow you to rip just the main movie if you like. Again, all this is explained in the guides.
Once you have the movie to the correct size to fit onto a blank, single layer dvd, you can use a program called ImgBurn to do the actual burning to the disk. It is free to download and use also. The guides for ImgBurn are here: http://forum.imgburn.com/index.php?showforum=4