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As for the question of whether to use tables or CSS positioning commands for layout, and how search engines the both, the only difference is that with CSS positioning commands one can force the order of the text to be different in the document source and that displayed.
You can gain a reasonable estimation of what a search engine spider will detect by viewing your web page through a character-based browser such as the freely available 'Lynx'.
Tables get read by SE's just fine... I don't know where you "learned" this but I'm sure you misread it... you're talking about what, 60 or 70% of existing websites not being searchable by SE's? Do you think the major e-commerce players would put up with their table layouts if they weren't getting indexed correctly in SEs?
And yes, CSS is hypothetically better, for two reasons.
1) As previously mentioned in this thread, you can use absolute positioning to feed SE friendly content first... not a practical possibility with tables.
2) CSS layouts, and the use of external stylesheets, SHOULD lead to having less code on your page than if you designed with nested tables and had inline styling. Of course, it's certainly possible to design a CSS layout that uses more code than a table layout, but if you know what you're doing, that shouldn't happen. Less code means faster spidering and a more appealing page to SEs overall.