Of some options mentioned (Remote Desktop Access, CrossLoop, and TeamViewer) here for remote access, none of them provide for recording a user's activity on their PC desktop. But, you can see what the other person is doing while you are connected to their computer. At least, I know that's the case with TeamViewer and, as I recall, with the Remote Desktop Access. I don't know whether that's true for CrossLoop; perhaps they can see what you're doing when connected to their computer but you can't see what they are doing.
TeamViewer is free for personal use; I've used it with my mother.