You've basically answered your own question by recognising that it's simplest to insert the media card into the card reader slot on the front of your PC. However you shouldn't expect anything to happen automatically. Go to 'Computer' and double-click on the icon for your media card. That will display the contents of the card. (In practice you might just see a folder at this stage. If so, double-click on the folder icon. If you see another folder icon, double-click on that as well. Eventually you'll see a list of, or thumbnails of, your images).
Once you've got a window containing your images displayed on the screen you can move them in the same way as any other files. (e.g. go to Edit and choose 'Select all'. Then click-and-drag the files to your 'My Pictures' folder).
Chris