The instructions for changing the resolution are on page 30 of the manual
If the pictures are fuzzy, increasing the resolution won't help. The most likely causes of fuzzy pictures are as follows
1) Focus. Check to make sure the focus is on the subject. If something else in the picture is sharp while others are not, then the camera may have focused on the wrong subject.
2) Subject motion. If moving objects are fuzzier than stationary objects then you need to use a faster shutter speed (or flash).
3) Camera motion. Just because the camera is on a tripod doesn't mean it doesn't move. One philosophy says that if a tripod is light enough to be carried then it's not sturdy enough. For a compact camera like the SD850 that likely isn't the problem. However, you can still shake the camera when you press the shutter release button. Try setting the self-timer. This allows time for the vibrations to die down before snapping the picture.
In your particular case, I think we can assume that the subject isn't moving, so #2 doesn't apply. To assure proper focus, make sure the painting is flat and perpendicular to the lens axis. If the painting is tilted relative to the camera, then different parts of it will be at different distances and the camera won't be able to keep all of it in focus.
Also, make sure the front of the lens is clean.