Important things:
Prompt Book - its a book you'll use to call the play. You'll write (in pencil!) all the light, sound, scene shifts, projection cues (if any), sfx cues, etc.. You'll also want to label french scenes (when actors enter and exit) and while they're rehersing you'll keep track of lines they drop. Some stage managers will hand out index cards with missed lines on them, others will just sit down and talk with the actors about it. (Ask the director about line notes if you have any questions) For the cues, many stage managers I know use multiple colors (one for each department, like lighting in pink, sound in blue, scene in green, etc.. ) or they use the sticky notes for arrows in different colors. You'll also have to note who wears what costumes, where which props go (and layout the props table), and you'll want to keep track of blocking.
Calling the show: During the run you'll call the show. When you do this, make sure you give stand bys and always gall the G-O as "department Go" A standby will either be like "Standby lights 5-15, scene shift 4, sound cues 7-12, and cue actors. Lights go, sound go, scene and sound go, lights go, send actors, lights and sound go, lights go" If its only a single cue just be like "standby light cue #' and then there will be a break before the cue (usually about 3-5 lines) 'Lights, go" Whenever you say a department and give the G-O, they'll go to the next cue, so be careful that they know who you're talking to.