Here's an attempt:
1. Don't Bog Everyone Down With Character Generation
When I have introduced people to JAGS I usually do it with pre-gen characters and have them pick them. In some cases I have a character with a couple of options (including gear) and let them spend a small number of points themselves. This is especially good with GATs ("Here is a list of 3 GATs for this character--you pick.")
2. Use The Character Generator. The one linked (or I can email you a file) is done in JAVA and produces HTML character sheets. It's not perfect but it's pretty good and should generate decent looking output. This will help players know how much damage they do and such without having to "do the math."
3. Have the Players Pick Gear from Lists. This is a best-practice for any game--but especially survival style ones. It generates excitement and energy (for reasons that I'll admit I'm unclear on--but I have some suspicions). Do I choose the blanket, flares, axe, and first aid kit? Or do I go with the shotgun and five shells? Do I get two walkie-talkies ... or a survival knife and flashlight? Stuff like that. That's less a JAGS thing and more a best-practice thing.
4. For Running Combat: Use a sheet of paper. Write everyone's name down the side including NPCs. Across the top is the Round number. When you roll Init you tell everyone to roll and then call out "+5!" ("I made my Init roll by 5") or "-3" or whatever. You write the numbers down next to their names and go in order of action. For groups of enemies just roll one for each group (say they are being attacked by 12 zombies, use groups of 3).
5. Use ADP for Foes. Keeping track of wound levels for lots of opponents is time consuming. So is keeping track of wound effects. If you give a Zombie nothing by 12 ADP it's either "fine" or it's "dead" (really and truly dead) and that's a lot easier.
For human opponents, a Major Wound, regardless of wound-effect, is enough to take most combatants out of the fight. Henchmen will be crawling away or surrendering if they're close to Injured or Serious condition.
6. Every Attack is 5 REA. This is a bit of a simplification but I'd use it to start with (exception: usually kicks stay at 6 REA). Don't load up on the Advanced or Optional Rules for a first time.
7. Use the Search Function and the PDF. If you own a printed set of rules? Great--but keep a laptop open with a PDF loaded and use the search function if looking for rules.
8. Avoid Grappling. The grappling rules are complex. Unless someone is really interested, don't worry too much. The one exception is, of course, zombie grabs. In this case pre-calculate grapple scores for the zombies and the PCs. As they are not action heroes their Defensive Grapple Scores will likely be around 12-16. If a Zombie has an Offensive Grapple of, say 14, that gives them a 12- to grab an ordinary character. Just have the table printed out so you can refer to it easily.
I'd even hand this out to them--the Zombie Stats:
- INFECTED BITE: 13- to hit, 1 try per Round, Must Have a Grab, 3 PEN. If you take 1pt of damage you are INFECTED!
- ZOMBIE GRAB: 13- to hit, 1 try per Round, Close Reach. Grapple of 14 (compare to your Defensive Grapple. If your Defense Grapple is a 12, it has a 12- chance of success if it hits).
- ZOMBIE BILE: 14- to hit, every other round, Acid burns for 8 IMP damage. GROSS!
And let them puzzle it out (you could even add some really weird stuff like CLOUD OF PESTILENCE that might not appear but could weird them out. Don't forget about RADIOACTIVE or BURNING zombies ...).
Put the damage table for each attack along then bottom so you don't have to calculate it during the game either.
9. Explain How The Dice Work. Train everyone to ignore 6's up front. Do a couple of practice rolls to show how it works.
10. Explain How Made It / Missed It By Works: If I need a 14 or less to succeed and I roll a 10 I "made the roll by 4." Often that's important and it's something that a lot of people seem to have problems with. Likewise, if I needed a 14 and rolled a 16 I "missed the roll by 2." In some situations that might be important.
I'm sure I'll think of other stuff--but that's all for now. Good luck! Let me know how it goes.