Since you're a new GM, just try to not get bogged down in looking stuff up at the game. You should keep a notepad handy though so you can write down questions you have to look up before you play again, because you'll have some questions that can't be answered immediately.
My first session DMing (D&D 3.5e), I didn't know how Attacks of Opportunity worked and I was giving them way too often. They occur when you leave a threatened square, not when you go into one. Oh well, I know now, and I knew for our second session too.
Try not to let the rules slow you down too much (I still have trouble with this), and have a good easy way to keep track of initiative when combat starts. It my first game, also played with people who hadn't played before, we took forever getting initiative order at the start of combat.
If you know what classes your players are playing, read-up on level 1 abilities of those classes before the game. Don't bother trying to learn every class 1-to-20 yet, just read-up on what you're actually using. (Include NPCs you plan to use in your studies.)
That's all I can think of off the top of my head.
Get the others involved as much as possible. For example, let one of the players track who has the initiative now. Or make the players remember who acts just before them, so they will know their turn is about to come up. That moves things forward more quickly.
I have a sheet where I write down the player's Will saves and AC. This way I don't have to ask the players if an attack hits or reveal that a spell was attempted (sometimes I do it anyway to make it clear what kind of foe they're up against, but I think it's more fun in game if not every player knows that player X has just failed a Will save so that means... (she's charmed, compelled, enchanted, etc.)
It's ALWAYS better to keep things moving forward than too drag it down while you look something up. Not sure what the benefit or penalty is off the top of your head. Give it a blanket +/-1 or +/-2 and keep going. AFTER the game you can look up the rule again and you'll probably be able to remember it better for next time.
Will the characters meet this NPC more than once? Give that NPC one quirk that will help them remember her. She brushes her hair out of her face a lot. One of his legs is shorter than the other. She's wearing two different colored socks. Doesn't matter... they'll remember.
Improvise for rules you don't know for sure, and look them up later as other's have said here.
Some specifics that can really help the first few sessions:
At level 1, the party is in more danger of everyone dying than usual. Hit point totals are just not that far from 0, so even a minor run of unlucky roles can kill the party. Don't let this happen - fudge a little if needed, allow healing spells to do max heal. Try to be subtle about it, but do whatever you need to do.
Have a cheat sheet for some of the stuff in the combat section (bonus and penalties when attacking defending - whatever looks relevant).
There is a special section in the back of the Core Rule Book that lists "conditions" such as staggered, dazed, etc. Have easy access to those as it's tough to improvise what those mean.
If you can, have a tablet or laptop ready with access to the PRD Rules Archive linked to on this site. That will help with the two points above.
If traps seem too much of a "save or get hurt really bad" mechanic, they are. Feel free to make trap encounters much more interactive. Some level 1 modules like to pile on the traps, not sure if Serpent Skull does or not.
Some general advice for the game:
Focus on letting the player's ideas work, instead of just putting up roadblocks in a robotic way. It's easy when starting table-top RPG games to constantly find yourself saying "um..no, I guess you can't do that". Just let some things go at first. Be honest that you're starting out somewhat of a "safe mode" and learn together.
Players having motivation to have fun with their characters or role-play their characters decisions goes a long way. It makes the encounters (and the campaign) much more enjoyable.
There is a really good section of two paragraphs or so toward the very beginning of the Core Book which basically states that: The rules are a guide, not a rigid system. Do what makes sense to you and what seems fair. The game is about having fun adventuring.
General Advice would be to always have something ready. Have a list of names/races/classes/quirks/professions ready. That way when the players go off course (they will, guaranteed) you can quickly look at the relevant information and cross it off the list.
As said keep D20 site open and ready for fast reference on a phone or tablet.
Set time limits on players after the first few sessions, if they don't have a spell ready, drop them in initiative to keep the game flowing. Slow players looking things up will bog a game down.
Do not waste time looking things up yourself, make cheat sheets, have stat blocks queued up, have a few maps/random encounters/loot tables ready. When a player is slow they can be skipped or moved, when a GM is slow the game stops.
Loot is more than gold. Art, antiques, trade goods, furniture, mundane items, fancy/exotic weapons, gems, animals, can all be used in place of gold and silver for loot. 100gp value silver horse childrens toy has no player wealth impact if it replaces 100gp worth of coins. But it adds flavour to the encounter.
Buy a boogie board or a dry erase board. Initiatives can be tough to keep track of (delayed actions, spells, allies joining, etc). By putting the players in charge of Initiative and setting it up in a place all can see, then everyone will know when they are next (and it is one less thing for a GM to keep track of).
Make certain everyone knows what resources you are using (and everyone has equal access to all of them). There are a lot of books, modules, etc for pathfinder, keep it fair.
Only use character names when addressing players. Keep out of game talk to a minimum. Bored players waiting for a wizard to roll 10D6 plus SR and concealment during concentration is inevitable, try to keep it to a minimum or they might remain distracted through their own turns (and affect other players trying to RP).
Agree to the games tone. silly? Serious? RP heavy? Experimental? Min-Maxed? Low-magic? Hardcore? Hero Fantasy Casual? Make certain everyone is on board and in agreement.
I also encourage you to avoid fudging dice too often, I roll 2D20 and take the roll I like (if the Boss gets 2 1's then so be it, the dice have spoken). Fudging can lead to railroading, and railroading can lead to saying no to PC's. Railroading should be limited to keeping PC's on story.
The one thing I say to anyone who's running a game is this: prepare to be surprised. Your players will do things you aren't expecting. When it happens, don't freeze up, just try to deal with it as best you can. Since you're running a module you have some constraints, so work within the limits it provides.
Most of all, don't worry too much, just try to have a fun game. :)
One I like to keep around,
"The best ideas sometimes come from your players".
Sometimes you'll have what you think is an A-1 humdinger of an encounter cooked up, and someone will say "Oh man I hope this isn't a swarm of bees that are on fire" or something like that, then you know to say "funny you should say that, because suddenly you hear a drone of insect wings, and the room temperature seems to grow hotter as a glow comes down the hall".
