I've heard tables are best to be avoided when going web standards. Some claim not. How do I know when to use tables and when not to?
That depends on what type of information they will contain.
If it's tabular data (like spreadsheets or calendars) or other clear data differences between the cells (like application forms) — stick with tables. But if all you want is nothing more than a list of images, links or text — horizontally or vertically aligned — use ordered or unordered lists instead, to be styled and positioned later on.