I said ''Simple'' didn't I?
That was!
Here's roughly how it all works.
Compressing a jpeg - which is already a lossy medium - doesn't usually achieve the desired effect. But any image manipulation software has a setting for 'resolution', and that's what you need to look for.
The reason is simple: on screen, we see images that are 96 dpi (dots per inch) as clear, but if we were to print those images, they wouldn't look as good, owing to our brains' ability to compensate for what we see on screen. Thus, to print out a photo, for instance, you would need to set the resolution to 300 dpi.
When you take a pic on your camera, the software you use on your computer makes adjustments to show the entire image on your screen at the lowest resolution, but it doesn't change the resolution of the original image, which will be pretty high - usually between 300 and 600 dpi. What you have to do, in effect, is to make a copy of the image in a much lower resolution, so it displays perfectly on a screen.
It's very simple, once you understand the relationship between 'size' and 'resolution'. Also, to help you out, most image manipulation software has a little percentage box somewhere at the bottom, which can be set to 100%, and when you do that, you can see just how large the image really is.