If you do not see anything on your desktop, this may be because your drive is not recognized by Linux. Either the partitions are unformatted/non-existent, or that the file system on the storage device is unknow.
Immediately after having connected the device, get to a shell, and enter the command
lsusb. This should list you the detected USB devices. You should see yours. It could be recognized by its brand name for example.
dmesg command should tell you about recent hardware detection.
Finally, run GParted, from the system menu. If you do not have it, get installed using Synaptics. GParted will scan for all devices it can detect, and will list them. You should recognize it by its size. Note that the numbers may be a little bit off, as there may be a difference between 1GB = 2^30 and 1GB = 10^9.