Working with an agency is a partnership and the best way to work together with a business is to understand their business goals so you can try to ensure your own are working in tandem.
A creative agency sells the time of the people in the company. This means, the more time the agency spends on your account, the higher your bill! This is not something to be worried about - it's just something you should understand. Look at an Agencies portfolio of work. If you're asking for a similar style to X client or the same functionality as Y website, there's a good chance the creative process will take less long.
Write a general brief and you'll get a relatively high price. Write a specific brief and generally you'll get a lower price. This is because, agencies sell time and if you know what you want and come over as a decisive client the ageny will believe that the creative process will take less long. If you come across as an unconfident prospective client with a broad brief, the agency will have to charge more to figure out what is best for your business.
There is a saying among project managers that the key to our success with clients is to 'manage expectations'. Don't 'over promise and under deliver'. Having worked both sides of the fence (buying creative services and selling them) the best way we have found is to ask for a finished piece in good time for whenever you need it. So, if you've got a deadline for an advert you might want to tell the agency your deadline is 1 week before that date. Work the agency hard to meet your 'deadline' and then (if you need it) you can say you've negotiated an extension for any important alterations.
Help to make it feel like one. Encouraging creative people to produce better and better work is the best way to achieve amazing results. Have fun!