You can select an Image to be shown at your pages/posts/slider/news by uploading from your computer or choosing from your Media Library for each Post/Page.
How to set a Featured Image?
Via menu at the post/page editor page.
What size should it be?
Size of a Featured Image may vary from theme to theme but it should be big enought for your current theme. Upload biggest Image into Media Library and WordPress will take care of the rest. Use the same dimensions for your featured images to have a better result. Run plugin Regenerate Thumbnails after switching theme.