Miriam,
As stated before the
line between sound designer and sound engineer is a fine
line and more often than not, handled by the same person. If you have a script (your lucky if you do, usually I find myself designing as I go) look for things that you would consider background or "audio scenery". Consider the settings. If the show is set in a
park, outdoor noises like birds and bugs would help set the scene. In a city, find car sounds or traffic noises. As you read the script, think about the actions that are going on. If the script calls for someone to
drop plates, a good designer would have a sound
cue for the crash of dishes. In theory, any significant action would have a sound associated with it. As a designer it is your job to develop all these sounds into a cohesive show. On some shows, it may even be the designers job to find stuff to make sound cues with also. I once had to design a show with an old time radio scene. I ended up building a mock-up of an old radio, and supplying music that matched the time period for the radio to
play. You should also consider pre and post show music, background themes, and live musicians if you need them for an
orchestra piece in operas or musicals.
Your director may have a lot to say about what they want to hear in particular scene. Or, they may let you run with it. Of course, some scripts have certain cues already in them. That doesn't mean you are limited to those cues though. In my experience, playwrights who direct their own plays tend to have very specific ideas about what they want.
Once your show is designed, it needs to get distributed to your audience's ears through a correctly assembled sound
system. That would be the sound
engineer's job. As a sound engineer you would look at the designers information and the venue the event is being held in and come up with a sound system that can accurately reproduce the material. This includes the right playback devices, a console with enough inputs and outputs, the right number, size, and design of the speakers and many other things.
Then you need an A1 (head sound tech)to actually run the show, and an A2 to help the A1 find the donuts......
Best of luck
Think about it like this. A designer (weather a sound or light designer) thinks about what some thing should sound like, or look like and is part of the creative process. An engineer's job is to make the designers dreams a reality.