I'm assuming you want help with connections to the touchscreen, not with making your FEZ look like a keyboard to the computer (or with configuring a keyboard as input for the FEZ, depending on your project).
There are essentially two options: Use ADC (analog-to-digital converter) lines on your FEZ to directly connect to the touchscreen, or use a touchscreen controller IC to do the low-level stuff and then connect with SPI or I2C to the controller to get the digital data.
The first option is cheaper (you don't have to buy anything special), but will take more processing time on your FEZ, and will require you to do a little bit of analog design work. Atmel's appnote AVR341 is a good reference, and easily translates to other microcontrollers. Page 7 gives some good requirements: You need a fairly accurate A/D source, 15-25mA source/sink currents, and a processor capable of taking new measurements 70-200 times per second. I'm not sure how well the FEZ works with frequent interrupts like that, so the second option might be more attractive.
The second option eases the processing you'll have to do. Chips like TI's TSC2200 even go as far as to give you a keypad interface so that you can simply wait for the chip to tell you that someone's pressed a key (it's 4x4 keys, not a keyboard!). However, the more features you ask of it, the more complexity will be present in the interface. For a .NET application, you probably want to see an interface rather than connecting right to the hardware,
Regarding the suitability of a touchscreen interface, consider that it can be uncomfortable to type on a rigid surface for a long time, and resistive touchscreens are even worse because you need to apply significant pressure. Don't expect to sustain high typing speeds for very long without causing pain in your fingertips. Also, you'll want some kind of feedback mechanism. The Apple iPod/iPhone/iPad screens are as nice as they are because they (1) indicate the letter you're touching and (2) increase the sensing radius of letters that are likely to come up with predictive algorithms and dictionaries. It's very hard to get a touchscreen keyboard to feel natural.
I'm just spit ballin here but why would you connect RL to LR if you've connected RT to UR?
Swap UL and LR connections and see what happens. It just seems like you would connect the L's to the L's and then obviously SG goes to wiper, so that leaves the U's to go to the R's so put RL and UL together.
I can't find any documentation related to the touchscreen mentioned so this is the best I got.
Best Answer
No. The edges of a resistive touch overlay are important. They carry the conductors that connect to the resistive layers.
Those white traces around the edge are conductors, and are necessary for the overlay to work. If you look carefully, you can actually see which wire corresponds to which axis and side.
Keep in mind that you can always use an overlay that is larger than your screen, as long as you have an enclosure that will fit/hide the excess overlay. You can simply scale the input position to ignore the outside regions.