What are some of the more important steps a contractor should take when starting a project in occupied areas?

Building in an occupied area can seriously complicate a construction project - but certainly not prohibitively so. If you are the client, I would ask for a detailed schedule as to when the contractor plans on performing all the aspects of their work - for example shutting off the water, bringing in large deliveries, turning off the electricity, etc.

Ensure that the contractor is employing proper temporary protection and barricades. If they are doing drywall, for example, they should be installing temporary plastic partitions to prevent the spread of the drywall dust. If they are doing overhead work, such as on a roof, they should rope off a perimeter around their work to prevent anyone from getting hurt by falling objects. The Contractor should also be cleaning up after themselves at the end of each work day.

If multiple people will be in and out of the work site each day, take the time to meet each of them so you can feel comfortable with the workers in your space.

The most important part is ensuring the safety of the people occupying the space. Never hesitate to ask the contractor to do some additional work to make sure no one will be in direct harm.

barricades, hvac close offs, ventilation, temporary walkways (dust and dirt control)