Jayeff linked to the only video/instructions I can find for disassembling the HDX. However, there are a few things they don't mention in the video, that I think would be helpful -- probably way too late to help Cynthia. When you are prying off the black strip on the back top of the Kindle, note the speaker locations. The speakers have tiny (~1" X .5") tympanums which are easy to damage. Do not push your prying tool under the speaker grills. There's no glue there any way. That may have been obvious, but I put two tiny scores on one of my speakers. It seems to be fine, but I could easily have torn it. Second, under the camera and light/flash, the shiny black strip has three tabs/prongs that perpendicular to the flat part of the strip that stick into the tablet. They are tiny little nubs about 1/16" - 1/8" wide and maybe 1/16" tall (extended from the flat). If you pry directly under the camera, you are likely to either fold these tabs up parallel to the flat part of the strip, or break them off. Be careful in...
A couple of years later, a less expensive solution is to get the Sintech PA6007 1.8" ZIF/IDE to mSATA adapter and mount a standard mSATA SSD on it. The Sintech adapter is about $15 on Ebay, $20 on Amazon, and I've seen it as low as $10 around the web. The interfaces are all proper, but I'm not sure if there are power demand issues. 240GB mSATA SSDs have been turning up at Holiday sales this year (2013) as low as $130 -- mainly at Amazon and Newegg. So for under $150 one can get 240 GB of storage. Of course, just before the Toshiba MK2431 was discontinued, one could get 240 GB of much slower storage for ~ $75.