www.bluerobot.com has some useful templates for some basic CSS-based layouts, which can be good starting points for different designs. www.htmldog.com has one of the more readable set of HTML and CSS tutorials, in my opinion.
Also, I'd just like to point out that CSS != DIVs. DIV tags can be useful at times to group related elements together so that you can apply a style for that grouping, but CSS can be applied to any HTML element. For instance, if you just have one paragraph of text that you want to position at the top right corner of the page in a box, you can just apply your style to that paragraph - there's no need to create a styled DIV then stick your one P element inside of it. I mention that here just because I see a lot of people who tend to suffer from "divitis" when they first start learning to use CSS styling, sticking way too many unneeded DIV tags into their markup.
Also note, somewhat related to the preceding paragraph, that if you are creating the sort of layout where you might have used image slicing before, with CSS absolute positioning and other aspects of CSS, you may not need to slice up your images (or not as much). You can simply create one main container div which has your entire image as its background, then position various other HTML elements within that DIV as desired to overlay particular parts of that image.
PS: Take a look at www.csszengarden.com when you have some time to poke around there. Every design there uses the same exact HTML source code; it's just the CSS stylesheet that changes. It will give you lots of examples on how to lay out pages using CSS (but there are no tutorials or explanations, just examples).