Ohio's primary election will be held on March 4th.  In order to participate, you must be registered to vote 30 days prior to the election.  The cutoff date is this sunday.  I don't have the full list of places where you can register, but I know that you can at public schools and the BMV, which means there isn't much time.   
Remember, if you have moved since you last voted, you will need to reregister!