How does a person become chairman of a congressional committee?

The Majority Party Leader selects the committee chairs. This selection process relies heavily on party loyalty. The Speaker of the House of Representatives is elected in a similar fashion. The party that is not in power selects its own leaders of committees, called "Ranking Members." 
That's how it happens most of the time, and above is the correct answer. However, the House of Representatives has the final say in how it conducts its business, and there is no prescribed constitutional method for selecting officers. The House could change the House Rules (not legally binding since they are not "laws") at any time.                

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