You could simply take one of the examples and play around with it for a bit, so you'd see what SFML can do and what you have to do on your own.
For a background image, you'd take a sf::Texture and a sf::Sprite, load your image into the texture, set the texture on the sprite and draw it every frame iteration.
If you don't change the view of the RenderTarget things will get automatically scaled when you resize the window, but the aspect ratio is not preserved, thus in most cases you'll want to change the view accordingly. For more information about the usage of sf::View you can check out
my tutorial on the wiki.