Let's assume a client want an album cover designed a typical order of events would be. First I would contact the firm and speak to the Receptionist and ask about my job. They would phone through to the Account Director. They would come down and we would talk about exactly what it was I was looking for in the design, and fill in a job sheet, which would help him work out how long the job would take. At this point he may to work out the price of the job.
All his notes would go into the job bag and then would get sent to the design studio where the Art Director would set the job to a designer who he thought could do the job and was free. If the best designer for the job was not free they might need to move some of the work about.
After the designer has researched the project, ideas would be presented to the client using a selection of mock-ups of proposed designs. They will take on board the response to these, and try to incorporate the best elements of all ideas into the final design, whilst considering constraints of practicalities such as price, packaging format etc.
Once the final design has been produced it may be appropriate to review again, although it may also be that this would incur additional cost.
At this point the design is signed off. Once signed the client can't change their mind or the design, and at this point they will have entered into a legally binding contract where payment has been agreed. This helps protect the interests of all parties, both in terms of meeting deadlines as well as limiting costs.