3 passes here.
Surprise works like this:
Rolling it up.
You roll the same dice as you would for initiative. If it is an ambush, the ambushing party gets +6 dice and can never be surprised by the party they are ambushing. If its a situation where some characters know there is a threat and other characters do not, then the characters who are aware of the threat get a +3 on their surprise test. Otherwise, it's Rea + Int + whatever initiative bonuses you might otherwise have.
What them dice mean.
Anyway, the number you roll determines who surprised whom. If you roll 5 hits and someone rolls 4, then you've surprised that person. If someone rolls 6, then they've surprised you. If they roll 5 too, neither character surprises the other. Again, an ambushing party can never be surprised.
What does it mean to be surprised?
Well, if one character is surprised by another, then that character can not respond to any of the actions the surprising character takes that pass. If shot at, the surprised character does not roll reaction and can not dodge. They go straight to soak. The surprised character can not return fire either, regardless of their initiative. This surprise state lasts for the first IP of the first CT only. However, for that pass, whoever has the highest surprise score can act with impunity. No one can target them and anyone they target can not dodge their attacks.
Effect on initiative?
None. A person can act first and surprise no one, or act last and surprise everyone. It's not likely, but it could happen. Four guys could surprise a mook, but the fifth one does not. In that case, the mook can only target the fifth guy. If a character can not act on any enemies or has nothing to respond to besides actions he was surprised by, then he loses that pass.