If you are not familiar with old-school D&D, the second-best introduction to these concepts is the D&D Basic Set Rulebook, part of the B/X edition of the grand dame of RPGs. I'm going to straight-up pimp that product out right here: B/X is the most elegant and well-explained edition of D&D that has ever existed. That book is five bucks. Play three or four sessions of it with a DM that uses all of the rules as written (or do it yourself), including encumbrance, turn-counting, light sources, random encounters, reaction rolls, and morale rules, and you will suddenly understand why all those things exist. If you are like me, you grew up playing D&D and ignored all those rules, and thus thought they were boring and didn't understand why they exist. You might still hate them after playing that way, but you'll understand how they interact, and it's a much more interesting piece of game design than its usually given credit for.
In any event, I make reference to those rules.
SurpriseThis one is the easy one. When two groups of similar size run into each other, you roll 1d6 for each group. If either side rolls a 1 or 2, they are surprised for the first round. I personally don't always roll for this. If a small group is creeping up on a large and boisterous one, the smaller group will not be surprised, and can probably get a look at the other side. They may or may not surprise the other side if they actually attempt to attack them.
In the case of surprise, the unsurprised side gets one round of actions, which may or may not be hostile. If the surprising side successfully uses stealth instead of attacking, or chooses to attempt evasion, the surprised side may never become aware of their presence.
Reaction RollsReaction rolls are of vital importance, because they help make sure you don't have to fight every goddamn thing you meet. Ignoring these makes old-school dungeon and wilderness adventures much too deadly. At least half of random encounters should be resolved peacefully, unless your players are actually looking for fights.
The way I handle these is a little different from basic B/X: You do not make a reaction roll until the NPCs or Monsters gain their first opportunity to act. PCs don't get to know how things are likely to play out until they start playing out. Further, do not apply any PC's Charisma modifier to the roll until they actually speak to the NPC or monster using a shared language or otherwise usefully communicate.
I prefer to do things this way because it forces the players to make a calculus of how they use a surprise round, for example. Do they open fire while the getting is good? Or do they have their Face start talking and apply their bonus? PCs in SWN will tend not to have quite so large of attribute bonuses available, and the PCs may therefore not have a character handy with a high Charisma bonus. If someone has substantial skill with Persuade, Leadership, etc., you might go ahead and give them an extra +1 to their charisma modifier when they share a language and can negotiate.
If the reaction roll is hostile but not "immediate attack," I'll usually let the PCs make their pitch and then apply any bonus they may have to whatever the original roll was. This does mean that a party with a good Face character will usually be able to avoid hostilities with random encounters, but I don't see that as a downside. There's always killer robots, assassins, and bioengineered horrors available if you don't want the PCs to talk their way out of every fight.
Considering the damage numbers in SWN, though, PCs have a lot of motivation to talk their way out of fights, and you should probably usually let them do it.
The PCs have encountered a quasi-tribe of exiled Lethix living in the eastern district of the ruined city, in the floating domed enclosure that they are currently exploring. They share no common languages, but the Lethix have an extreme predisposition to Telepathic abilities. The Lethix group has a sort of telepathic Shaman who has mastered the Level 2 telepathic ability to communicate regardless of language, and he has therefore been conducting negotiations. Right now, one of the PCs has volunteered to undergo "examination" to determine if they are truly friendly or if they are emissary of "Korgok," some sort of sinister supernatural figure or evil god that the Lethix fear.
It turns out that "examination" means the Shaman will be digging through the PC's memory in search of where they come from and their purpose. Since the Lethix are TL1 barbarians with no concept of a universe outside their little domed paradise, this is going to blow his mind.
This is a good step, because the Lethix can tell the PCs a whole lot about what is going on in the area, and thus entangle them in local issues and give them plot hooks.
Other stuff you should read:
Mark Gillham has done an excellent job of writing up his players' attempt at Hard Light, an adventure module for Stars Without Number. Hard Light is a pretty cool module, and his players sound like pretty cool guys.