How do you resolve surprise attacks in this system?

I couldn't find any such rule, nor anything useful under the stealth entry in the skill section.

PS. For clarity, by surprise attack i mean an attack by a character who is actively hiding from another character and then the hidden character attacks.

There is no rule. The way I handle the situation with ambush/surprise is I just have those being ambushed roll their initiative with a Difficulty to include upgrades and/or Setbacks attached depending on the situation, and the ambushers roll a simple check as normal. This way it's pretty likely the ambushers will go first, ie surprise, and maintain the advantage in a combat, which is essentially what happens anyway.

There are some that suggest opposed rolls with things like Stealth and Perception, or to do that and then roll initiative. I personally just prefer to incorporate it inclusively in the initiative roll and keep things moving.

If the PCs are setting an ambush waiting for some adversaries and there is the RPing going on then having them roll Stealth checks of some kind to determine how high the Difficulty/Upgrades/Setbacks will be for the adversaries is something you might try.

In addition to a Stealth check...

Remember that Cool is used by ambushers, while Vigilance is used by the targets. Cool reflects the ability to keep it together while waiting (no giggling, fidgeting, fart noises, etc). With that in mind, any Leadership or Discipline could also be used to boost the ambusher's Cool check, or make the Vigilance check more difficult:

- the Command talent adds a boost die to Discipline checks made by allies

- adapting Fire Discipline from space combat could also be a way to add a boost

- Inspiring Rhetoric (especially Improved and up) also add boosts

- Leadership can also be used to organize the ambush in the first place, as a well planned ambush has a higher chance of success

Depending on the circumstances you could also make cases for Survival, Streetwise, and other skills to come into play. None of these are really spelled out in the rules, but the openness of the system is a virtue.

What they said.

Attacker rolls a Simple Cool check for initiative. Targets roll a Vigilance check with a difficulty determined in any of the ways described above.

Depending on how the party described their actions, I could see giving one member of the party a free action as the "trigger" for the ambush. I suspect giving the entire party a free action would be too powerful; but giving one PC a chance to shine and/or do something stupidly heroic fits with the space opera genre, in my opinion. After that free action, you'd move right into initiative and structured play, but I really like 2P51's idea of adding difficulty, upgrades, and Setback dice to the target's initiative roll, while the PCs roll as normal.

Lots of good suggestions here; I'll just add my own idea. For a quick and dirty representation of an ambush, have the ambusher make a Stealth check vs. the target's Perception or Vigilance. For every one or two successes the attacker gets a boost die to his first attack, and for every one or two advantage he gets a boost die to initiative.