There are several parts to that equation:
1- The design professional or architect or engineer, who drafts the permit plans for you, according to all codes, good construction practices, and who deals with the structural part of the design -as well as electrical, plumbing, mechanical, architecture (the ways it relate with the existing house, interiors and exteriors)
2- Soil engineering: consultants that will analyze the bearing capacity of the existing soil and will recommend remedial steps in order to build the basement (the structural design will include underpinning under the existing bearing walls)
3- The general contractor, who will execute the necessary work to have your basement built.
4- I would recommend to have third party inspections to expedite the process and to see if there are problems that need to be addressed.
The general contractor will give you a list(s) of materials, will deal with actual site conditions, some of them are unforeseeable (maybe there’s a pipe or a tree root in the way, nobody knows) and he is bonded, licensed, and insured.
The first and most important part is to know how much do you plan to spend in digging up a basement, how deep, and how large in terms of square footing. Budget is very important, and to keep within its limits is crucial.
Take into account that the minimum height for an habitable space is 7’6″, plus a certain depth for a foundation slab and flooring. If it is intended for anything else than storage, you will need natural light and ventilation by code, the windows should be egress type to be approved, plus Co2 and smoke alarms.
There are also requirements for external entrances in historic districts, and you should plan for a future location for an internal stairs if you ever want to incorporate that unit to house in the future.
Hope this helps.