The above link has broken picture links but the text is accurate. Depending on the model you have there could be a number of different configurations. Some did have an option for an internal hard drive while most have a horizontal DOM, or disk on module. Its a special ssd that has an ide interface (that DT Research made slightly different on the pin out than normal ide headers). Its a half height pin header. Pics that should still be good here:http://webdt.org/forum/viewtopic.php?f=16&t=517#p2657
That link is to a hardware mod guide for putting in a off the shelf ide horizontal dom ssd. It will show you pictures of the hard drive, insides and essentially what you are looking for. Hopefully the first link helps out a little in taking it apart.
All the screws from the back hold the front bezel on. Once they are all out flip the unit, remove bezel, and take the rest out around the screen. Notate location of the one short screw. Pop the inner assy out from the back (I usually lay down a towel and flip the unit so the screen is in my palm). Once the inner assy starts to move pivot the case, hinging at what would be the top of the screen, over the top and open it like a book. There is a ribbon cable that you are not going to want to mess with so I use that as the pivot point and lay it down on the towel. On the back of the screen is the motherboard and on that will be the ssd.
Usually we can find power supplies on ebay. Someone on the forum here may have some kicking around too. Are any of the model numbers or serial numbers visible on the back of the DT's that you have?