It's easy to start up an improv group, since the only requirements are an empty space and perhaps some lights. Everything else is created from the imaginations of the actors and audiences.
You may want to consider having a concession stand with pop and snack foods. Once you're well-established, you might even start merchandising (T-shirts, cast photos, etc).
The person running the lights is, in a sense, a member of the cast. They can determine when the scene is over, and they can change the direction or mood of the scene by altering the lighting. In any case, good communication between the performers and the lighting person is important; usually a "lights down" gesture is agreed on beforehand so that cast members (even those not onstage) can let the lighting person know when to end the scene.
One simple technique that adds a lot of polish to the show is to bring the lights down after the suggestions have been taken, pause for a second, then bring them up again to mark them beginning of the scene.
The musician also provides pre-show music, and sometimes plays during intermission. If you have no musician, a tape can be used for these purposes instead. In any case, the music chosen for pre-show should be lively and upbeat, to raise the energy level of the audience before the show formally begins. The intermission music can serve to keep the intermission from dragging on too long (which saps the energy of the audience). In addition to all of this, the musician can provide little musical "bridges" between scenes.
If your musician uses a synthesizer, they can provide sound effects as well. If not, you can have a sound technician with a selection of short, leaderless (possibly continous-loop) sound effects tapes. Some troupes have a "foley artist" with a collection of sound effects devices (doorbells, gongs, buzzers, gravel with shoes, etc) who works the way old-style radio sound effects people did.
The host also keeps track of the time, decides when the intermission should take place, and wraps the show up at the end (thanking the cast and crew, and usually introducing them by name).
In some troupes, the host also sets up all the scenes, while in others, the performers take turns.
Troupes that use costumes will often build up a collection of assorted items, usually kept on a coat rack or offstage table.