Welcome to fly fishing. Where in NY are you? There's a lot of excellent steelhead fishing in NY around the Salmon River near Pulaski (north of Syracuse), and in western NY.
As far as when, salmon (chinnok and coho) are running now, with steelhead typically starting to trickle into tribs in Sept, but mostly the steel and big late run browns start to come up in Oct. Steel goes through winter too. Expect lots of crowds for salmon and early steel, but folks start to thin out (a little) as the weather starts getting cold, and thesalmon start to peter out in late Oct.
A lot of the fishing is flow dependent (dam releases on the Salmon) and it's best to check on conditions before going. Here's a daily report from the Douglaston Salmon Run (a pay to fish river access spot on the Salmon River):
Douglaston Salmon Run, World-Class Salmon FishingCurrent Conditions
If i was just starting out in FF and going after steelhead, I would get a guide. It's very specialized fishing, access to prime spots on good water, ability to read water, getting your fly to drift properly at the right depth. knowing the latest fish movements, knowing the best lies in different flow conditions, etc are all real important. A guide would definitely be your best shot at getting hooked into one.
I’ve never met with or fished with this guy, but know Loren by his reputation. He would give you a great experience and you would learn more in a day with him or someone like him then a couple of seasons on your own.
Traditional Fly Fishing Guide Salmon River-Pulaski and Syracuse areas of New York: Salmon/Steelhead/Inland Trout guiding photos articles
As far as rigging up goes, do you already have fly line? If not I would take your rod and reel into a fly shop and have them rig you up. I would probably recommend lining your rod up with an SA Steelhead 8 wt line (for rollcasting and the ability to withstand COLD water for winter fishing without turning into a slinky.)
If you already have the backing, fly line, and leader check out the fishing section of Animated Knots by Grog
Rigging would be arbor knot for backing to reel, albright knot for fly line to backing, albright knot leader to fly line.
You might also want to track down a local chapter of Trout Unlimited. There are a bunch of them in NY. They often run group trips for steelhead and trout, and it's a great way to learn a lot about FF instead of trying to figure everything out on your own. They also have informative meetings, and classes on tying and casting clinics.
Here's a general steelhead site so you can start reading:
Also be aware that the later in the winter you fish, the worse the conditions can be (hypothermia) and some water, like the Salmon River can be down right dangerous, especially in heavy flows. Korkers (slip on cleats) and a wading staff are a good idea (I think the DSR even requires Korkers after Nov 1)
Hope this helps.