Playing the Role of an Arkham Master in Arkham Horror?
You can find a good bit of info addressing your questions through ones already on the site: 

Keep the game running smoothly:
How can we play a shorter but satisfying game of Arkham Horror?

"Quick" reference sheet:
What do you recommend putting in an Arkham Horror quick reference sheet?

On playing a 'Herald':
What can I do to ensure that my friends&#39; first game of Arkham Horror with me is as awesome as possible?

But roughly, keeping people on task helps the game speed greatly. Having people know a general idea of where they'll want to move before their turn starts makes movement phase go much faster. It also isn't necessary all the time to make everyone wait for combat. If the outcome of the fight can't affect them, let them take their turn. Taking control of reading encounter cards for people helps trim down on the back-and-forth that can happen when the players don't know where each other are on the board. 

Before playing, the players should know:

A rough detail of the four phases


Upkeep: Wiggle sliders &amp; refresh cards
Movement: Move up to your speed. Stop at monsters &amp; fight if necessary
Encounter: If you're in a spot with a picture, get a card
Mythos: A new gate &amp; monsters show up. Too many gates and you lose


Skill checks: Number on the relevant stat + possible helpful items you have - number in the (). Get one success

Combat: Will check at the blue # penalty. Get one success. Then fight checks at the red # penalty. Weapons help. Need blood drops # of successes for combat

Gate closing: Go to a gate token, have a couple encounters where the token takes you, come back &amp; make a fight/lore check. Repeat to win

Clues: Can spend 1 clue to roll 1 more die. Repeat as desired. Also you need 5 to make sure a gate never comes back

If find they don't need to know specifically how many monsters can be on the board, how many can go in the outskirts, &amp; how many gates before losing. 8 players are going to need to be closing gates from the very beginning regardless.

For 'Herald' play I haven't done much more than drawing a few mythos cards and picking which one takes effect, drawing more monsters than necessary and choosing where they get placed, and not reading players the results of choices/success/failures from encounter cards before the result is decided.