Actually, Candace, a Realtor can help you find a rental home. Many are listed in the MLS. The Realtor will also help you with the paperwork (lease application, etc.)

You might want to check the website below to see if they have any rentals that might be interested in going long term.

Candace, sounds exciting! Prior to owning our own home we rented. Also, we are experienced landlords, so I can provide some general guidelines.

You might want to check out the state of New York's landlord tenant laws. I tried to insert the link but was prohibited.

A couple of key points:
Landlords are cheap, so I suggest driving around an area that you like, and looking for "for rent signs". If you are new to the area, you might want to consider renting something with the idea you can move once you understand how things work in your new town.
Without a doubt, craigslist.org is probably the most effective tool you will have. Other online sources should turn up in Google, (small circulation local newspapers are a good bet).
When you decide on a home make sure that you complete a walk through with the landlord and bring your camera! Take pictures of everything.
The landlord should have a written contract. Read it and make sure you are comfortable with the terms. Does it include gardener service, or are you responsible. Keeping the sidewalk shoveled, leaves raked, etc.
You will probably need a copy of your credit report, so you can download one and have it ready.
From your post I was assuming you are probably on a budget. However, it may be that you are a family with kids moving in a job-related transition. Local Realtor(s) are trained in lease arrangements, everything from one bedroom apartments to one acre estates. They are paid by the property owner, so go ahead and ask for some help. As I mentioned earlier, landlords are cheap, so if you are using a Realtor(r) know that the qualify of property (and price) is probably higher (although not always)

Generally when you rent a house you sign a lease for one year. After the 12 months is up the lease converts to month to month. Know the terms, how much notice you need to give if you plan on leaving in a certain time period. Depending upon your situation and local market you might be able to arrange a lease-option. A portion of your rent is allocated toward the down payment and purchase of the property. Check with a local Realtor for details.

Good luck.