A simplified crew

Director and Producer - Sometimes same person, better if they are different people... Director is in charge of the artistic vision and the performance of the actors, the producer secures the details and the finances.

1st Assistant Director - Scheduling and timing, keeping the production moving, mediator.
2nd Assistant Director - paperwork, runner.

Continuity/Wardrobe (this can usually be combined on smaller sets but you have to find someone committed to every day of the shoot) - Very detail oriented person!
Make-up Artist - exactly what they do

Director of Photography - Behind the camera at all times, decides the shots with the director (good to plan the shot list before the day of the shoot)
1(2?) Camera Assistant - moving tripod/other camera equipment. getting timecode for the shot list (since they are standing there this makes it easier)

Sound Head - knows sound well, sets the sound equipment up for each shot
1 Sound Assistant (boom operator) - helps the sound head and holds the mic

Lighting Head - Knows light and works with the DP to get the lights set up for the shot
2 Grips - Sets up lights where the light head tells them to and fixes other light problems for each shot.
2 Production Assistants - Runners, extra assistants and extra grips.

approx. 16 people on crew (pre-planning can help combine jobs)