After thorough review of applicant firms, credentials and experience data, possibly including direct contact with firm representatives if such can be arranged, identify the firm which appears most qualified to service your specific requirements.
Contact representatives of that firm believed to be most qualified and open negotiations to establish a mutually acceptable consulting fee arrangement and payment methodology. Most consultants are experienced in at least several types of retention agreements, including hourly fixed rate, fixed fee, cost plus fixed fee, percentage of overhead, etc.; usually one of these will be most suited to the type of work involved.
If the negotiations prove satisfactory, the client should at this point retain the consultant to ensure availability for the project. If negotiations are not successful, they should be terminated and opened with other qualified firms, one at a time.