How do I connect my mbed NXP LPC1768 to my computer. I have a USB cable and a breadboard. What else do I need? What connections do I need to make?
To expand on my answer in the comment above. Take your mbed out of the packaging and insert it into its' new semi-permanent home on your breadboard. Turn on your computer and connect your mbed using the USB cable which came in the box (or any other similar cable). As Rob says it'll show up as a flash drive called MBED, I've not used one on a Windows computer but I don't think you have to install any drivers (on Linux it's all ready to go out of the box).
On the mbed drive is a single html file, open this using your browser of choice and it'll take you to the mbed.org site and ask you to register (you have to register to gain access to the online compiler). The good thing about this process is it automagically attaches your mbed serial number to your registered user (you can't register without having a valid serial number at the moment).
The getting started instructions on the mbed.org site (and on the leaflet that came in the box) will walk you through downloading the compiled binary example to make LED1 flash on and off. Once you've downloaded it, copy it to the mbed drive, and press the reset button on the mbed (it's in the middle of the board) you should now have a fully functioning blinking LED.
Next have a look at the program in the online compiler and change it. Once you've got it going then you can start hooking it up to various external things. There are various instructions in the Cookbook and Notebook pages at mbed.org (including how to hook it up to a dual digit 7 segment display by me).
You will also need internet access (unless you have local tools installed) to compile and upload programs to the mbed.
Once plugged in check your computer and you should see the MBED as a USB drive/device. This will then have the necessary website access info you need to start working with the mbed.
See this pdf from Philips for further info.. http://ics.nxp.com/literature/presentations/microcontrollers/pdf/mbed.pdf