PostgreSQL and query planner
The most detailed discussion of how statistics are used is the Row Estimation Examples section of the documentation.  Ultimately all information about how a query might be executed is turned into a serious of costs via the various Cost Constants.  So if a table is 1000 pages in size, and the statistics suggest 10% of it will be touched at random by a proposed query, that's 100 pages * 4.0 (random_page_cost) = 400 cost units for pulling in the data; then other constants are used to determine things like processing costs on the data in those pages.

The query optimizer tries various ways of obtaining and combining individual components:  different join types, different ways to access the table data, etc.  It iterates through the possible plans from those combinations, then picks the one that has the cheapest total cost to execute.

I wrote just over 50 pages on this subject for my book PostgreSQL 9.0 High Performance, which has the longest discussion of query execution available right now.  There's isn't too much there on how statistics are used beyond what's shown in the documentation though.  Most of it covers all of the various query plan node elements you might run into.