Requirements for ISO 9001:2015 certification of a law firm is similar to any other organization. Having a quality management system designed and implemented according to the standard.
First, I would decide the scope of the quality management system. Is it applicable to all areas and services or just for some?
If you are starting a project to implement ISO 9001:2015:
Setup a project sponsor, a project manager, and a project team. Ensure top management support, get training about the standard. Designing and implementing a quality management system implies being knowledgeable about ISO 9001:2015. As a first step perform a Gap analysis, to determine the amount of work to be done - comparing what your organization already has in place versus ISO 9001:2015 requirements. From that GAP Analysis, you can develop your Project Plan, listing what needs to be done, by whom, until when.
From there it is implementation in order to close the gaps found. Then, perform an internal audit and the management review. There you can decide if your organization is ready for a certification audit.