Besides getting the call right in the end, what are the mechanics and order of making the calls?

 

Runner on 3rd and 1st, one out, 2-2 count and both runners moving on the pitch. The batter swings and misses at an inside pitch, but the pitch hits the batter's arm (not much of his arm) and rolls to the backstop. The runner on third slides across home while the runner that started on 1st rounds second while the batter is running to first on what appears to be a dropped third strike. How do you sort that out?