What the law says a tenant must do

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To your landlord the most important thing about you, as a tenant, is that you pay rent on time.
If you do not have a lease, your landlord can raise your rent by any amount he wants, if you are notified at least 30 days in advance of the next time rent is due. For example, assume your rent is due on the first of each month. If on May 15th you receive notice that your rent will be raised from $120 to $150, that is less than 30 days before June 1st, so the rent should not go up until July 1st. If you are required to make weekly payments, the notice period is 7 days, not 30.
It is a mistake to pay in cash, but if you do, make sure you get a receipt each time you pay the rent. Do not agree to have a receipt sent to you by mail. If you pay by check or money order, keep your cancelled check or your copy of the money order which will prove you paid the rent.
Besides paying your rent on time, you have other legal obligations as a tenant. In general, you must avoid damaging the apartment.

Specifically you must:

a. Keep your apartment or house safe and sanitary.

b. Dispose of trash and garbage in a sanitary manner.

c. Keep all appliances that the landlord provides in good working order.

d. Keep the electrical and plumbing fixtures clean and use them properly.

e. Not damage the apartment or permit your guests or visitors to do so.

f. Not disturb other tenants.

g. Except with good reason, permit your landlord to enter your
apartment if you get at least 24 hours notice.

h. Make certain that you, your family or guests do not violate Ohio’s drug laws.

You are responsible to your landlord for any damage you cause. Your landlord can take the money out of your security deposit when you move out and sue you for additional damages. However, you are not responsible for normal wear and tear (for example, walls that routinely need to be repainted, or plumbing fixtures that break down because of long use.).
Your landlord can ask a judge to evict you if you do not perform your obligations. To evict you for violation of one of those obligations, you must receive written notice of the violation. If you do not remedy the condition within 30 days, your landlord can begin an eviction action in court.
If you make repairs to the apartment, your landlord will not be required to pay you for the work you did except according to a written agreement or if you can convince the Court that he made a promise to pay you.