I've been asked to add a video from a DVD to a Joomla website and not sure how to go about converting the files to flash.
Any help is greatly appreciated.

The contents of the DVD are as follows:
VIDEO_TS.BUP
VIDEO_TS.IFO
VIDEO_TS.VOB
VTS_01_0.BUP
VTS_01_0.IFO
VTS_01_0.VOB
VTS_02_0.IFO
VTS_02_0.VOB
VTS_02_1.VOB
VTS_03_0.BUP
VTS_03_0.IFO
VTS_03_0.VOB
VTS_03_1.VOB
VTS_04_0.BUP
VTS_04_0.IFO
VTS_04_0.VOB
VTS_04_1.VOB
VTS_05_0.BUP
VTS_05_0.IFO
VTS_05_0.VOB
VTS_05_1.VOB

Before we begin, you need to know that there are a myriad of ways to recode DVD content - I will only cover a few of them.  If you have a choice in the future though, avoid getting your source material on DVD (ask for .mpg, .avi. or .wmv instead).

First, lets assume that the contents are not copy protected (it's not a commercial DVD).

Your main goal is to convert the VOB stream to a DeCSS-free MPG-layer2 stream.

1.
One way to do this is to use TMPG Encoder Studio.  Specifically, use TMPGEnc XPress.  This allows you to select a VOB stream (usually the largest file size(s)) and convert it to an .mpg file.  Depending on the size of the source material and the speed of your computer, this could take up to a couple of hours or more.

With the .mpg file created, your are free to manipulate it in any video editor and use any of a number of different encoders to convert to .flv.  Riva makes a free encoder that works OK.  If you can afford it, Sorrenson Spark is a wonderful reencoding package.  If you want to be sneaky, get an account with Brightcove and download their encoder/upload package.  If you use it to encode/upload a video, you can copy out the .flv file which is stored (in a location that I decline to disclose since this is probably illegal) before it is uploaded to the Brightcove server and cleared from its cache.  This is great because you can get a 2-pass on2-vp encoded .flv stream (excellent video quality) for free...

2. Purchase somekind of DVD - mpg/avi/wmv conversion software like DVD2PocketPC or PocketDVD or PocketDVD Studio, etc.  This makes it very easy convert selected video streams into an easily manipulable file format.  BUT, and this is a big BUT: stay away from converting to Xvid .avi, because most editors don't know what to do with it and most conversion software will not recognize it.  This has to do with it's high-compression scheme.  You're better off converting to .wmv.  Oh, and make sure that you're converting to a HIGH Quality video file, since the quality will be substantially reduced by the time you convert to .flv.

3.  If you browse the web, you will find many open-source .vob-to-.avi conversion tools.  Just follow the instructions and all should work OK, but the process has a steep learning curve for newbies. 

So, just remember that the whole point is that you have to go through 2 conversion processes:  VOB to avi/mpg/wmv and then to flv.

You are MUCH better off getting the source DV tape or mpg/avi/wmv files or whatever, than being handed a DVD.  xVid, Dvix, and mp4 are NOT great files for further manipulation/conversion - they should be considered the end result, like a flash video file.

Oh yeah, one more thing:  Any programs that claim to convert DVD to anything other than mpg, are still actually converting to mpg as an intermediary process before converting to any other format.  As an example, the TMPG program I discussed above will provide you with an EXACT COPY of the source video in mpg format.  This is as good as it's going to look/sound before you compress it further into an .flv file.

Thanks for the help!  It is greatly appreciated.
I will ask for the source files as the content is not copy right material.  It was developed by the school.