What you can do is draw everything to a rendertarget with a nice resolution. Say 1280x720 (a lot of games use this resolution or lower on the consoles). You then get the texture from the rendertarget and stretch it over the entire screen (you might want to add Anti-Aliasing as a post process step when upscaling). When you you stretch the game to a non-widescreen resolution you should add black bars on the top and bottom.
This approach works fairly well, and is easy to implement. But if you want to support a very large set of (odd) resolutions (say 640x480 to 1920x1080) you have to make sure the text and everything is readable by testing the game at all resolutions. Btw don't use anti aliasing when downscaling as this will actually worsen the image.