I have come across this question a couple of times and it has been very fun doing it but yesterday I came across a number that required me to write open score into short score but half way I realized the alto note I was about to right was going to be higher than soprano note. What should I do in that case??
I guess you mean compressing 4 staves S-A-T-B onto 2 staves SA-TB. In this case you write the S and T notes with stems up, and the A and B notes with stems down. If the voices cross, well, you have to make sure the result is neat and readable. (This is why for more complicated music 4 staves are normally used.) If you use Musescore, for example, simply make the S and A separate voices, and everything happens more or less automatically. You also have to hope there are no crossing stemless notes (semibreves), because then you are stuck.
You show which voice is which by the direction of the stems, and position the note heads as in the picture.
If you have whole notes with no stems, you can move them horizontally, to make it clear the parts are still crossed.
If that might still be confusing, you can add "leader lines" to show where the individual parts go.
And if you are writing the sort of music where the leader lines might be mistaken for glissando marks, give up and keep the open score! Sometimes in orchestral scores, the parts for instruments like two flutes are mostly written in short score on one staff, but in open score in the systems where short score would get too complicated.