Open BaseCamp and plug the GPS into the computer with the USB cable. Wait for BaseCamp to recognize it. It will appear under the "Devices" heading on the left side of the screen.
Click on "Internal Storage." The Waypoints saved on your GPS will be listed in the window below.
Select the Waypoints you want to load. To select multiple Waypoints at the same time, hold down the SHIFT key or CTRL key while clicking the ones you want. Once you have all the Waypoints you want selected, click File > Export > Export Selection:
Your computer's save dialogue will pop up. BaseCamp will save all of your Waypoints as a single file. By default, it will be saved as a GPX file. Make sure to save the file someplace you will be able to find it again.