There are four basic cases:
- style= attribute. This is the least maintainable but easiest to code. I personally consider use of style= to be a bug.
- <style> element at the top of the page. This is slightly better than style= because it keeps the markup clean, however it wastes bandwidth and makes it harder to make sweeping CSS changes, because you can't look at the stylesheet(s) and know what rules exist.
- page-specifc css: This lets you have the clean HTML and clean main CSS file. However, it means your client must download lots of little CSS files, which increases bandwidth and page loading latency. It is, however, very easy to maintain.
- one big site-wide CSS: The main advantage of one big file is that it's only one thing to download. This is much more efficient in terms of bandwidth and latency.
If you have any server-side programming going on, you might be able to just dynamically combine multiple sheets from #3 to get the effect of #4.
I would recommend one big file, whether you actually maintain it as one file or generate the file through a build process or dynamically on the server. You can specify your selectors using page-specific IDs (always include one, just in case).
As for the answer that was accepted when I wrote this, I disagree with finding a "combination of classes that gives you the result you want". This sounds to me like the classes are identifying a visual style instead of a logical concept. Your classes should be something like "titlebox" and not "red". Then if you need to change the text colour on the user info page, you can say
#userInfoPage .titlebox h1 { color : red; }
Don't start applying classes all over the place because a class currently has a certain appearance that you want. You should put high-level concepts into your page, represented by HTML with classes, and then style those concepts, not the other way around.