Vincent is correct, BUT most region templates have a "clear: both;" style applied that undo's the floats. So simply adding the float is not enough. You'll want to add a "clear: none;" to counteract the clear: both. Hope this makes sense.
I setup this example:
I also added another technique which is to add regions with divs before, in between and after your regions and those are the ones that contain the floats. It's a little more work, but this technique can be used for much more complex layouts.
Hope this helps.
Another common issue with subregion layout is the use of No Template/legacy theme templates that don't contain the necessary HTML mark-up and/or substitution strings to support static region IDs, #REGION_CSS_CLASSES#, or #REGION_ATTRIBUTES#.