Design and implementing a quality management system (QMS) for a mechanical engineering firm implies being knowledgeable about ISO 9001:2015. Now the standard is less and less bureaucratic, it is up to each organization the task to design, develop and implement its QMS.
Setup a project sponsor, a project manager and a project team. Determine the scope of the QMS, your organization may decide to include only certain lines of business. Ensure top management support, get training and 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.
Then, an important step is to design a model of how your organization work as a set of interrelated processes. For example:
Decide how to describe and monitor those processes.
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.
This is a very short description of the journey but below you can find more detailed information: