Just like the MEMO structure in SQL Server which is kind of a "paper trail" of steps the optimizer takes in optimizing the query. Is there anything in MySQL through which I can get the information like, which plans the optimizer considers, the cost of each plan?
The recent 5.6 version has added this feature.
You can see it in action in SQL-Fiddle. Not sure how the output can be beautified.
The best I can immediately mention is to simply run EXPLAIN on a query.
There is a graphical way to do this
As for steps to optimizing a query, a parse tree is created. Rather than explaining the parser here, please read my post from Mar 11, 2013 (Is there an execution difference between a JOIN condition and a WHERE condition?) on what the parser does.