how does one start a head hunting/ staffing business?

1) Incorporate, including business plan (fee structure, industries
etc), finances, payroll, bank accounts, insurance etc.

2) Find employers who are looking for employees (want ads, past
employers, friends etc).

3) Find canidates - 

4) Screen and match canidates to positions  - submitting resumes for review.

5) maintain and build relationships with everyone.

You should probably have a knowledge of the industry to be able to
adaquatly screen canidates and jobs to ensure a good match.

You may consider purchasing a Franchise, Management Recruiters comes to mind.