There are three principle methods used for breaking up stylesheets: property-based, structure-based, and hybrid. Which method you choose should most be based on workflow and personal preference.
Property-Based
The most basic, representative form of a property-based breakup would be to use two stylesheets: structure.css and style.css. The structure.css file would contain rules that only used properties like height, width, margin, padding, float, position, etc. This would effectively contain the "building blocks" necessary to arrange the elements of the page the way you want. The style.css file would contain rules with properties like background, font, color, text-decoration, etc. This effectively acts as a skin for the structure created in the other stylesheet.
Additional separation might include using a typography.css file, where you'd place all of your font properties. Or a colors.css file, where you'd place all of your color and background properties. Try not to go overboard because this method quickly becomes more trouble than it's worth.
Structure-Based
The structure-based method of breaking up stylesheets revolves around segregating rules based on what elements to which they apply. For example, you might see a masthead.css file for everything in the header, a body.css file for everything in the content area of the page, a sidebar.css file for everything in the sidebar, and a footer.css file for everything at the bottom of the page.
This method really helps when you have a site with lots of distinct sections on each page. It also helps minimize the number of rules found in each stylesheet. Unlike the property-based method, which tends to have a rule in each stylesheet for each element on the page, with this method you only have one rule in one stylesheet for any given element.
Hybrid
As you might expect, the hybrid method combines the best of both methods and it's my preferred choice. Here you create a structure.css file, just like in the property-based method, using only those properties that you need to create the basic layout. Then you create additional stylesheets like masthead.css, which skins the header; body.css, which skins the content; etc.
Other Considerations
One problem that plagues each of these methods is that by creating multiple stylesheets, you require that the client's browser fetches many files. This can have a negative effect on the user experience because most browsers will only make two concurrent requests to the same server. If you have seven stylesheets, that means adding potentially hundreds of milliseconds on the initial page load (this effect is lessened once the stylesheets have been cached, but you want to make a good first impression on those new visitors). It's for this reason that the CSS sprites technique was created. Breaking up your stylesheets may wipe out any gains made by using sprites.
The way around this is to compress your broken-up stylesheets back into one stylesheet when the user makes a page request.
To get the best of both worlds, consider using a CSS meta-language like Sass. This allows a CSS author to break one stylesheet into many while still only presenting one stylesheet to the browser. This adds a step to the CSS authoring workflow (though it could potentially be scripted to compile the Sass into CSS any time a Sass file is updated), but it can be worthwhile, especially when considering some of Sass' many other benefits.
