There is a lot of information available about permits and the permit process on the BDS website. You may want to look at the Commercial Alterations or the New Users section.
Be aware that commercial permits for work of any complexity are not generally issued "over the counter". That means that you must provide the city with four sets of plans, pay part of the building permit fees up front, then turn the plans in for review.
Staff representing the various groups with an interest in development (building, zoning, fire, transportation, sewer, etc.) will be assigned to your project. Any reviewer who looks at your plans and needs additional info/corrections before signing off will mail you a "checksheet" telling you what they need. The city's goal is to get all of those checksheets to you within a couple of weeks.
To respond to a checksheet, you will go to Document Services, which is on the second floor (above the DSC). You will need to update all four sets of the originally submitted drawings, either by replacing the original sheets with new sheets or marking changes on the originally submitted sheets. Keep any replaced sheets with the new sheets, and mark them "Void".
When all the corrections are made, the reviewers will check the changes made. When all the reviews are completed, it takes several days to process the paperwork. Then, you pay the rest of the fees and the permit is issued. Licensed contractors will need to apply for separate permits to do the electrical and plumbing work.
When all the inspections (building, mechanical, electrical, and plumbing) are approved, and the card you are given at permit issuance is all signed off, then the space can be occupied.