Are you literally downloading the videos or are you getting a video stream? If the video really has been downloaded to your HD then you have it and can use other programs to manipulate it (save in another format, clip certain scenes, add your own soundtrack, etc.)
If the video is being streamed to you then your options are more limited. Many pay sites have switched from a download model to a streaming model because streaming videos are harder (for casual computer users) to capture, save, and share!
In either case you need the right software... but do you have it? People often think that their computer (Mac or PC) can't do X. That is almost never true; most often you simply don't have the necessary software.