Being new to UW Photography, and to post developing of images, I have a few seemingly simple questions.
Hi Greg, the simplest questions are usually the hardest, but I'll take a crack at it.
1. When you download from your cam card, you get the JPEG and the DNG. I'm assuming the DNG is the RAW image that I want to work with? If so, what format do I save this file in when I export? JPEG? TIFF? Other?
This depends on your camera, I'm not sure what type you have so I'll guess you can get the DNG (digital negative) format straight off the card. This is a form of Raw capture developed by Adobe and only adopted so far by a few camera manufacturers. My Canon for instance uses the Canon propietary form of Raw. You want to work with the DNG format or your camera's Raw format in Lightroom to make all your adjustments. Then after adjustments you can export the file in the format that will depend on what you intend to do with the image. For the web JPEG's are great.
2. Is there a methodology or order to which settings should be changed first as far as lightroom tools?
A fundamental about Lightroom is important to understand here. LR never changes your original Raw file. It creates a list of the adjustments you want to make and stores that list in a seperate or side car file that stays with the image. The program was designed for you to start at the top of the Develop menu (white balance, exposure) and work your way down the menus. The cool thing is though that since the modifications you make are contained in the side car file they are applied in the "correct" order each time. This way you really don't have to worry about it. You can jump back and forth until you get the image you want.
3. What is "Too" much when it comes to photo manipulation?
This is the tough one, everyone is a little different. Some would say any manipulation is too much. There have been a few lengthly discussions here on the subject. Do a search for threads about manipulation and you'll see what I mean. If you mean what I would call processing, (those things you do in LR to clean up your image and help it to look like your eye intended) then it's a little easier to answer. Most beginners like us tend to over cook the controls, especially with saturation and sharpening. A good place to start is to move the sliders over until you think it looks good them back off a little.
Color is tough too, it's relatively easy to change the blue background for example with LR, it's also easy to create a color that you would never see in the ocean. I'm constantly impressed by the discrimination of colors demonstrated here by the pros. They are constantly working to get more accurate colors, especially the blues.
Don' worry, you'll pick it up in no time, I found it very helpful to go to Adobe TV and watch the free videos there on Lightroom. It's fun to watch what the software can do in the hands of a master.
At the end of the day they are your images, if you like them then they're perfect. 
Have fun,
Steve