Would changing the O2 sensor when my check engine light comes on resolve the problem?

There are HUNDREDS of things that can trigger the check engine light.

Step ONE is having the trouble code read. That tells you were to start looking for the problem.

The easiest issue to fix is not properly securing the gas cap. There are also at least a dozen different sensors that could be the culprit.

Again: Have the code(s) read. Don't just throw parts at an unidentified issue.

We could all vote what it might be. Would you accept the results or kick and scream if the vote doesn't come out the way it should. 

Auto parts stores get rich off of people who keep guessing what is wrong and replace parts that their car doesn't need instead of knowing what is wrong.

Have someone at least hook up a code scanner to the engine PCM outlet and get some clue as to what is wrong. Most auto parts places will hook up a scanner for free. 

A respectable shop will hook up their $4,500 scan tool to it and will know more precisely what is wrong. 

Only if that is the problem, have it scanned and fine out. It could be a loose contact that needs to be pushed on better or a sensor replacement. Have it checked before you start replacing things!

Code readers are about $20 these days.

Don't guess. Go to an auto parts store and get the codes read for free.

That could be the reason your light came on, but there are at least a thousand other possible reasons.  You need to go to Advance or Auto Zone or the like & have them put a scanner on it to retrieve the code.  If it is an O2 sensor, change BOTH of them on whichever side is bad.   I have read that a brand new O2 sensor will take it's partner down if it's got a lot of miles on it.

Get a scanner and read the trouble codes.

You didn't mention which error code you have or any unusual symptoms. If you don't know how to diagnose the problem yourself, don't fire the parts cannon. That could end up being more expensive than getting a shop to diagnose the problem and implementing the correct solution the first time.

Only if the O2 sensor is the problem.

How about instead of throwing parts at it, you get a reader and pull codes.