Reference for Supersampling
EDIT: I took this answer down for a time because I realized a lot depends on whether there are any idiosyncrasies in how images are mapped to pixels by actual devices, and, not being an image guy, I don't know a lot about that.  I decided to bring it back, with the caveat that the answer may be insufficient given said idiosyncrasies.


  The image should be upsampled before supersampling. But how much?


You are just trying to soften quantization (pixel resolution) error by collecting information from neighboring pixels.  Thus, oversampling by a factor of 2 should be plenty.  In other words, once you oversample until your sample resolution is twice that of the pixel resolution, nothing can be gained by oversampling more.


  Is there any special filter to be used for upsampling prior to supersampling?


I might be misunderstanding the terms, but it appears to me that upsampling is part of supersampling.  No, you don't need to use any special filters.  Insert 0's in between your samples and then low-pass filter.  You'll probably need to adjust the gain of your low-pass filter by your upsampling rate to get the pixel intensity to come out right.


  What if I want to resize image to e.g. 80% of its size with supersampling?


Then factor that into your upsample/decimation calculations.  After you upsample you have to decimate down to the pixel resolution.  By resizing the image you are, in effect, changing the pixel resolution.


  How much I have to upsample it and how to treat non-integral size ratio?


How much you have to upsample it depends on the details of the image, pixel resolution, etc.


  How much I have to upsample it and how to treat non-integral size ratio?


You can deal with non-integral ratios with fractional resampling.  Essentially you upsample by an integer and decimate by another integer, giving you a fractional sample change.