It sounds like the problem you are having is a pretty classic one. There are a lot of great designers out there, ones that we may respect and admire, but they don't know the first thing about the business of doing design work.
When looking for a designer, pay close attention to not just their blog design, but to the names on their portfolio. Who have they worked for and how they solved design problems for them matters just as much as the quality of their work.
A "good designer" should know how to work with you, to reflect your vision and walk you through (hopefully) an iterative process of design. They should communicate their approach pretty early on, telling you how they plan to solve your design/user interaction problems and let you know exactly what to expect.
And for the record:
Any design project should start with Information Architecture (IA), usually meaning sitemaps and wireframes and hopefully a prototype of some kind. You may not think you need it, but this is a crucial first step to "design." It allows the designer to reflect your features in a lightweight deliverable, making sure you are both on the same page. One they can quickly iterate on to flesh out the user interactions.
(Any client that comes to me with wireframes already done, usually costs more not less, as we still need to go through the process in order for me to get up to speed. If they are already done it means a lot of design decisions have already been made without me and they will be very hard to undo for the sake of the users best interests. A seasoned designer comes with a lot of experience and best practices, which can help considerably on any project.)
IA should be the bulk of a design engagement and will entail a lot of back and forth with you, and should start right after a brief getting to know the project period, typically called "Discovery." If that doesn't happen consider it a red flag. Scheduling can be a problem at times, but the schedule should be understood on both ends at the beginning.
After IA comes Design, which is typically done in Photoshop, which is great for creating designs, but major changes can eat up a lot of time (and money). It is crucial that the layout, navigation and interactions are all agreed to (and don't change) before design begins.
If you are skinning a web app and doing design in parallel, then you need a good CSS designer, and Photoshop can be skipped, but that is an entirely different type of design project. You can use a junior level resource here, but it could take more time and iterations than a traditional design process. For this type of project I might recommend a designer that has a good rep for creating skins and themes.
A good designer will limit the number of "comps" or unique designs you do as well as the "rounds of revision" per each design in the estimate and contract. I never recommend that you ask a designer to do more than one comp, it only multiplies that cost and the client gets little extra in the end because of it. (It's like telling the designer that you know more about design then they do and they often produce one good design and two shitty ones because of it. Any client asking for multiple comps is a red flag to me that approval is going to be a pain in the ass, and they often get charged accordingly.) Instead look for lots of rounds of revision so you can work iteratively to get that just right design.
That all being said, understand that design is very subjective. A good designer knows this and has an approach to figuring out how to create the right design for you and more importantly your users. You should get a sense of this right away, if not, then ask them how they plan to create it. Be honest with them about your tastes, your internal stakeholders and most importantly listen to your designer and their experiences. And for god's sake treat them as an equal partner and not as a slacker art school student.
The design of your product will be one of the most important decisions you make. It will establish the first and often only impression of your product that your end users will make. I've seen it a hundred times over a bad initial design can be a very costly mistake, costing a lot more to undo. It establishes trust and understanding of how your product will work. And remember that design isn't a perfect process, but a good designer should get you a hell of lot closer to your goal.
You'll notice that I haven't really answered your question. It sounds like you need to think a bit more about what type of designer you need and what they need to do for you before moving forward. Once you figure that out, getting a designer to suit your needs becomes a lot easier.
I have a few related articles I wrote about the business of web design ages ago, but should still be relevant, that should hopefully help understand the business of designers a bit more:
http://flingmedia.com/articles/pricing-a-project/
http://flingmedia.com/articles/the-agency-model-is-dead/
Good luck.
-Brian