DVD movies are required to have .vob files broken into 1gb chunks. So it is normal to see several .vob files with one movie.
Converting dvd movies to avi is not particularly hard anymore and there are many different programs that can do this. AviDemux is a free one.
Here is a very basic guide for using the program: http://forum.videohelp.com/threads/295782-How-to-get-started-with-avidemux-edit-and-convert-any-video-format
Basically you just import the VTS_01_1.vob, let the program join and index the files, then set your output codecs for both video and audio. A normal choice would be Mpeg4-ASP Xvid for the video and mp3 for audio. Use an avi container (under Format) and use a name for your new file with an .avi extension.
The default output size when using these settings would be 700mb, but you can increase the output size by clicking on configure once you select Xvid for the codec. A larger output size, say 1.4gb, would help the overall quality of the video. Or you can change bitrate. It is quite flexible on how the encoder works.
Here is the home page for AviDemux, where you can download the program: http://fixounet.free.fr/avidemux/
Edit: By the way, this program will only work on unencrypted dvds. If you are working with commercial movies, you'll need to decrypt and rip them to the hard drive first, before converting.