The best process would be letting the broker who helped you buy the house, of if you bought it without a broker then a broker from the neighborhood, list the apartment for you. More than likely if one has bought a multi-family house one expects to offset some of the cost of the purchase with rental income. The broker will do things you could not: 1) Appropriately price the apartment according to the neighborhood market, 2) run credit, 3) demand and examine the prospective tenants' financials, 4) show the apartment at all hours, etc. It's important for a landlord to remember that this is a financial situation, and a good broker will have a process to determine if the prospective tenants can meet the financial demands of the apartment. Most importantly, this should be of no cost to you. It is customary in New York for the new tenant to pay the broker's commission on the rental of an apartment, so all of this expertise will be free of charge to you.
Please let me know if you have any further questions.
Dan Brady, Corcoran.