Here are a few tips for new GM's (not just new to Edge of the Empire - new in general). Hopefully some other GM's will add their suggestions as well. Enjoy!

Paint With Broad Strokes

Don't spend more time developing locations than you need to. Hoth is a snowy ice planet. Tattooine is a desert world and Coruscant is a planet covered by a city. This isn't "Star Trek" where you might want to detail your Class M planet for the science team - keep your worlds simple. The same goes for locations, whether it's a cantina or a safehouse, a few sentences can set the location's key features in the players' imaginations without you spending a lot of time. If you need a map for miniatures combat, give the players enough detail so they know where there are opportunities for cover and some exits and some options for hiding and sneaking. Don't add a lot of set dressing to your maps (unless you enjoy that part of adventure design).

Central Casting Is Your Friend

Unless you need to create a unique, memorable character, use stock characters whenever possible. A Gamorrean thug can become a Gamorrean speeder mechanic. A medical droid could become an intelligence droid, or a bartender. Don't spend time statting out NPC's who likely won't see combat, and if combat happens unexpectedly, grab a handy stat block and run with it. Your players aren't going to know the Sullistian arms dealer who just drew on them is using an Aqualish thug's stats, they're just going to know they are dealing with an angry alien with a blaster.

Use The Dark Side

Just as players can spend a light side Destiny Point to add to their skill checks or fill in a missing piece of equipment, the GM should feel free to spend a Dark Side destiny point to make their adventure a little more difficult. If the party has chased a suspected assassin to the top of some tall building, the GM could simply decide the villain has a grappling hook to escape with - there's nothing stopping the GM from just doing that. However, the game provides a mechanic for this that not all role-playing games do with the Destiny dice pool. Perhaps you need this villain to appear later in the adventure - by all means give the a way out - but by spending a Dark Side point, you provide the players with a Light Side point they can use in that final battle to do something really special. Maybe they'll even take a page from you and spend a light side point so that one of the players has a grappling hook in their utility belt - the villain doesn't automatically get away, but now you've limited the pursuit to one PC and the rest of the party has to take the long way around to head them off. Whatever the situation, use the flow of Light & Dark destiny points to keep the action moving.

Reward Creative Role-Playing

Your players will, frequently, come up with an idea that is so crazy and off the wall that you couldn't possibly have planned for it. Wing it and let them try. In fact, give them a bonus for coming up with a creative answer to a problem, especially if they can pull off something cool without firing a shot. Think about Han Solo, presented with a stolen AT-ST thanks to Chewbacca in "Return of the Jedi". Anybody could have just gotten into that thing and blasted at the bunker until they got in. Instead, Han puts on the pilot's helmet and convinces the Imperials inside the bunker to open the door. THAT'S ROLE-PLAYING. When you and your players remember their tabletop glories in the months and years to come, they aren't going to remember that time they rolled a natural "20" in a fight, but they will remember the time they convinced an Imperial astromech droid that they were covert ISB agents and it started sabotaging the Star Destroyer's tractor beams and cannons to aid their escape!