You would require a USB host. I dont beleve its possible with just a PIC18. The PIC18s with built in USB are USB slave devices only.

If I was you I would look for a USB host chip that you could interface to a PIC. Perhaps something like this: http://www.maxim-ic.com/datasheet/index.mvp/id/3639

If you are only going to be using the USB thumb drive for storage, a simpler solution would be an SD card because it is much easier to interface to a PIC.