Wow, Chris, your post sounds exactly (I mean, word-for-word) what I would have liked to post to a forum like this when I started flyfishing... but that was before Al Gore invented the internet. Fortunately for you, this is a great place to get advice.
While there are a lot more knowledgeable people on this forum than I am, not many of them have started their flyfishing careers in Ithaca, in September, just after having graduated from college, without any help whatsoever... but I have. In fact, I remember distinctly getting skunked my first 10 trips to the stream, and we're not talking hour-long jaunts, either - we're talking 30-40 hours on the stream. On my eleventh trip to lower Salmon Creek I finally landed my first little snapper, and that started a hot streak - one fish each time for FOUR consecutive trips! Good thing I wasn't relying on flyfishing to eat, but it sure was fun, even then. As I look back and consider my abilities at the time, I am reasonably certain that those were the four stupidest fish ever stocked on an Eastern stream.
David's giving you FANTASTIC advice. The flies he mentions are consistent producers, if fished correctly, anywhere you go - hard to beat that list of patterns for just starting out. So I won't try. Just do what he says.
I would also advise you to find someone who knows what he's doing to show you the ropes - and not just some friend who beats the water alongside you, find someone who really knows what he's doing. I could spend 5 minutes showing you how to nymph and you could catch fish that way for the rest of your life (I think there's even a proverb about it...), or you could spend 5 years on the internet and in books and never really have a clue as to what you're doing. Remember, there's a very fine line between zero fish and ten fish, so find a guy who routinely catches ten fish and ask him to show you how he does it.
Streamers are easiest because you don't have to worry about line control so much - jerking the fly around sloppily can even induce strikes. But, ironically, you'll never consistently catch a lot of fish on streamers in a stream. A hint with streamer fishing, though, if you want to stay that course: Get the fly down by whatever means necessary. Only the most aggressive fish are going to come flying to the surface for a streamer in the dead of winter (although I've had it happen, spectacularly, with large fish before). So buy some split shot and change weight continually to suit varying water conditions and to probe different depths of the water column. Once you've learned effective line control (much, much easier said than done), managing weight is the single most important factor in catching fish subsurface.
I floundered around on my own for many years catching very few fish. Then I was fortunate enough a number of years ago to have been shown how to nymph by an amazing fisherman who happened to marry my aunt (years too late, from my perspective), and it has totally transformed my fishing. When you watch a master of the nymph or dry, it is like watching someone practice voodoo on the fish. You may even watch silently and think you know what he's doing, but in reality you probably have little clue... unless, that is, you can convince him to take the time to show you what he's doing and he's a good enough teacher to iterate what he intuits.
My parents still live in Ithaca, so I might be able to get together with you in a few months and show you what I know. But there are a ton of great fishermen in Ithaca - just find one willing to help you and you'll be on your way.
-Shawn