Once the virtual com port driver is installed, the USB programmer board should show up in the device manager as a com port. It should have a number greater than 2, such as COM4.
There is a simple to use graphical flash utility for the LPC2000 series microcontroller made by Philips. You can download the program from the LPC2138 page (it is towards the bottom). Once installed it is pretty self-explanatory. You will have to specify the com port, and the .hex file to upload. You will also have to select LPC2138 as the device, and a crystal frequency of 14.7456 MHz. A baud rate of 115200 will give a speedy upload.
Connect the Critter Board to a power supply, and then connect the USB programer baord as in the picture. There are two slide switches on the USB programmer board to select run and program modes. When the switches are in the program mode (towards the USB connector), the computer has the ability to reset the LPC2138 into bootloader mode. Make sure the switches are in the program position.