Lets imagine I have this code:

<div class='A'>
    <someSection class='B'>
        <nestedSection class='C'>
        </nestedSection>
        <nestedSection class='C'>
        </nestedSection>
        ......
    </someSection>

    <someSection class='D'>
        <nestedSection class='C'>
        </nestedSection>
        <nestedSection class='C'>
         </nestedSection>
    </someSection>
</div>

What styles must I declare to make sections B and D display side-by-side (like they were in two adjacent columns of the same table)?

Well a lot of ways to do that. Maybe float one to the left and float one to the right. Or you might use this bit posted by chrishirst:
http://www.webmaster-talk.com/css-fo...tml#post363166

Helped me figure out what I needed to do.

As Tom said there are a lot of ways you can set up columns without tables. Floating B to the left is probably the easiest, but it will depend on the entire layout of the page as to what's the best.

other thread on same problem

http://www.webmaster-talk.com/html-f...ight-side.html

Originally Posted by chrishirst

other thread on same problem
http://www.webmaster-talk.com/html-f...ight-side.html

I started that thread also. Thanks for the answers... But float is such an headache, that I ended using tables...

Ew, tables

Originally Posted by ehentai

I started that thread also. Thanks for the answers... But float is such an headache, that I ended using tables...

Not as hard as you think. Don't give up so easily. A table isn't the right way of doing it.

You might also want to consider a using a list or definition list. Lists can be very flexible for that sort of thing.