Hi Tim!
"Rent" is the money one pays to the landlord.
It is not usually used with "a".
Example: "I have to pay the rent tomorrow." "Did you pay the rent?"
Because the speaker is talking about his/her specific rent payment, "the" is used with the noun.
"Renting" is the progressive form of the verb "to rent". This word isn't used as a noun in American English, so it won't need "a".
Example: "I am renting an apartment in the city.
"A rental" is a noun for any house, apartment, trailer, car, boat, bike, etc. that is available for rent. A person may pay rent to use it for a specific length of time.
Example: "That house is a rental." "My car is a rental."
I hope this helps!