What steps should be necessary to optimize a poorly performing query?

I know this is a broad question, but I've inherited several poor performers and need to optimize them badly. I was wondering what are the most common steps involved to optimize. So, what steps do some of you guys take when faced with the same situation?

Related Question:
What generic techniques can be applied to optimize SQL queries?

What is optimization query optimization methods?

Query optimization is the overall process of choosing the most efficient means of executing a SQL statement. SQL is a nonprocedural language, so the optimizer is free to merge, reorganize, and process in any order. The database optimizes each SQL statement based on statistics collected about the accessed data.