If you've made sprites at a low resolution, they become smaller when you change to a higher resolution. To counteract this, scale your sprite at runtime. Just bear in mind: if you do this, you won't see a difference between the high and low resolution, because you're simply scaling a low resolution sprite. This is only useful if you want to adapt to 16:9 screens as well as 4:3.
If you want your sprites to look PRETTIER at a high resolution, just draw them in that high resolution by hand, and scale them down if you are using a lower resolution.
By scaling down, I actually mean rendering them at a scaled size at runtime. Don't create multiple assets for multiple resolutions. That's insane.
I mentioned 16:9 and 4:3. When the ratio between the width and height of the screen changes, you'll have to decide for yourself how you want to handle that. At some point, you've decided to show a certain area of your game world on screen. If I change from 4:3 to 16:9 (or any other widescreen format), are you going to add some viewable area to the sides of your already viewable area, or are you going to cut some parts off the top? In other words, you'll have to decide for yourself if you need the width to stay the same, or you need the height to stay the same.