The first thing to start with are the requirements and goals of your web project.
1. Do you target only a mobile audience?
If you want a Web-App, you'll need more than a CSS framework, a mobile framework that combines look and feel for specific target devices' UI with functional elements by means of Javascript. The next decision will be if the framework better supports smaller smartphone screens, tablet screens or both.
If you don't need the more functional Web-App approach the way to go are frameworks that are responsive. You will have to concentrate on how you want to arrange and order certain page elements on different screen resolutions and what page elements can be turned off on the smaller resolutions. (This sometimes leads to political debates with the stakeholders debating around what is (more) important and what not).
2. Do you target both mobile and desktop audience?
You want a framework that supports reponsive or fluid layouts for greatest support of your audiences clients. If the graphic design you have to produce is more static the responsive route suits better as it allows easier planning in the different stages within the breakpoints. Most designers currently follow flexible approaches, lightweight, elegant, presentational, not-so-portal-like that also allow fluid implementations (where certain or all page elements are allowed to stretch or grow according to the client/browser viewports).
3. Do you target only traditional audience?
Then simply choose the framework you're confident it allowes the easiest implementation. Did the designer use a grid? Then maybe the CSS framework fits it. Some CSS frameworks come with a nice variety of design templates for Gimp, Photoshop, Illustrator and others, so maybe the design can be based on the template upfront which allows for the best realization.
Two other considerations:
A. There is no graphic design
If you start without explicit design templates I would choose a framework that allows for easy integration of Typography, offers lots examples, use cases, pre-defined page elements or components (buttons, navigation, thumbs...).
B. Time constraints
No time? Some frameworks come with their own or third party customization scripts or wizards. Choose the elements or components you need, turn on or off certain JS libraries, reset stylesheets, things like that and download the final package. That's it.
Some frameworks are pretty mature and well tested so the absence of a vibrant community may not tell you that much. Depending on your skills a lot of support may not be necessary (and even be a bad sign: The grid/framework should be simple and stay out of your way. The questions that may come up should so be the usual CSS questions that are quite common and can be answered even without details of the underlying framework).
Two examples to illustrate two approaches (more grid <-> more responsive):
http://960.gs/
Definitely take a look. Follow the "view the slides" link to read nice background information. A true grid system. It also links to derivatives that support fluid and elastic looks.
http://twitter.github.com/bootstrap/
Modern, nice hype. Lots of components. Customizable. Responsive.
Web-Apps:
http://jquerymobile.com/ and http://www.sencha.com/products/touch