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?
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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.