Assuming you've installed the Audacity software, first check your recording device. If you use Windows, first check the Audio Control Panel. For Windows 7, click Start > Control Panel > Hardware and Sound. Under Sound, click on the Manage Audio Devices link. In that window, click on the Recording tab. Select the USB option and make it the active device.
In Audacity, you may also need to make sure that this is the recording device that is active. That should be the third drop down from the left in the Device Toolbar. (If it isn't visible, click View > Toolbars and check it.) The Device Toolbar is right above the recording trace section in my version of Audacity.
Now click Record (the red circle) and start your turntable. Do you see a change in the trace? You should see a flat line for up to 10 seconds and then see this change to a set of high and low values.
If you don't get this, check if your USB ports are working. If you use a USB hub, try a direct connection. Check the device manager under Universal Serial Bus for a triangle with a red x or a yellow triangle. Try updating the driver by right clicking on the device. Also check Windows Update (for an optional update) or your computer manufacturer site for a new driver.
Unfortunately with the USB, you can't hear the recording as it is made. Do a short recording and then stop it. Then play back the selection. Adjust the input volume level lower if your trace is hitting the top of the box. This is clipping and your recording won't include the full signal from your record.
I've used Audacity for recording cassettes through the line in port. You can do this with some turntables if you add a pre-amplifier and use RCA to 3.5 mm adapter. Connect to the line in on the back of the desktop (blue).
If you could not install Audacity, go to http://audacity.sourceforge.net/
to get a version that works on your computer's OS.
I hope this helps.