The mbed Application Board makes it very easy to get your LPC1768 connected to a network but it is not absolutely necessary if you are comfortable using wire strippers. The mbed 1768 has all the electronics needed to connect to an ethernet network with the exception of an ethernet jack. This technique will work for connecting the LPC1768 directly to a switch with a short Ethernet cable but is a slightly "off-label" use and will probably not work for longer cable runs or in noisy environments.

If your cable is wired according to the standard it will have an orange and white striped wire on the far left with a solid orange next to it as shown in the picture below. You can make the connection by cutting an ethernet cable and wiring 4 wires from the cable to 4 pins on the mbed 1768.

If the colors of your cable follow the standard you will connect them as in the picture below with the solid green connecting to the 5th pin down from the top right, followed by the green and white wire connected to the 6th pin. The solid orange wire connects to the 7th pin from the top right and the orange and white striped wire connects to the 8th pin down from the top

Connect the other end of the cable to a network switch then connect the USB cable to power the board. If you made the wiring connections correctly, the switch will indicate your board is connected. My Ethernet cable is only about a foot long and it connected to a D-Link switch sitting on my desk without any problems. If you need to run a longer piece of cable you should add a proper Ethernet jack as shown on page 69 of the datasheet for the Ethernet PHY chip included on the LPC1768 mbed board. The 4 resistors and 2 decoupling capacitors are already included on the LPC1768 board.

TI DP83848C datasheet