If you do not have a written rental agreement with the person, and he/she is not on the original rental agreement with the landlord, then the law treats them as having an oral lease agreement with you (i.e. they are the tenant, you are the landlord). Therefore, you will have to follow the steps of a formal eviction process. Most local courts have forms and pamphlets for landlords to assist them with handling their own evictions without legal representation. However, you should know that the process is very strict and if you do not follow all proper procedures, you may not be granted an eviction and could potentially be sued by the tenant for wrongful eviction. If you are unsure of what you are doing, you should consult with a knowledgeable attorney in your area to ensure you are following the process correctly.
Best of luck.