It's not always easy to tell, because so many things have probably been restained and painted over the years to colors not natural for the species, but if you research the area and the time the house was built, those alone will probably narrow it down a lot to likely things like pine, or oak, etc. You can Google just about anything now (with "Images") if you word it properly and maybe the local library could help with good pix.

Your first clue would be the region in which you live.

It comes from experience in seeing and working with different types of wood. You go by the grain and the colour of the wood. Grain is usually the biggest clue.

These sites have some nice samples of different wood types.

http://home.howstuffworks.com/guide-to-furniture-woods-ga1.htm

http://www.hardwoodinfo.com/species_guide/display_species.asp

You often have to strip the wood in an area that won't be noticable -- closet, for example, although sometimes they put cheap wood in the closets. Oak, birch and maple were commonly used during that time.

You can also verrrrry carefully pry off a piece of molding (say, a bit of baseboard in a corner behind a door) and take it to a specialty lumberyard or woodworkers' supply store like Woodcraft. If you can take up a bit of wood flooring from a closet or under a threshold that would be ideal as well. The people who work in those places tend to be more knowledgeable by far about identifying wood. Other woods used for millwork and flooring in that period and style include Douglas fir, chestnut, elm, walnut, cherry, and other fruit/nut-woods, mahogany, gumwood (eucalyptus), redwood, pretty much you name it... it all depends on the original builder's tastes and budget, and what was readily available locally (unless someone wealthy wanted to show off with exotic woods).

To complicate the issue: it's also very common for the public areas of the house - living and dining rooms, front hallways, foyers, etc. - to have the "extra fancy" wood for mouldings and flooring and the private areas such as kitchens, bedrooms, and upstairs hallways to have completely different, cheaper materials, although the "cheap" wood of 100 years ago is still miles better than a lot of the expensive stuff on the market today! (Which is why it's such a sin to rip it out willy-nilly and chuck it in a dumpster.) We know this is the case with our ca.1900 house; although we have not begun stripping the trim in earnest enough has chipped off all on its own for us to know that the downstairs trim is a tight-grained hardwood that had started its life with a very dark finish, while the upstairs trim is pine or spruce that had originally been painted a rather gruesome minty-yellowish green, almost more like an opaque stain.

And to even further complicate the issue, in that period labor tended to be fairly cheap due to widespread immigration of European craftsmen and the materials were dear, and there was a good bit of "faux bois" grain-painting going on (yes, even in A&C houses)! So something that once stripped turns out to be pine might not have originally appeared to be pine, it might have looked like a much more expensive wood like mahogany or gumwood...

It will be difficult to learn to recognize wood types by looking at a photo in a book, or an image on a computer screen. You might consider visiting an antique store, and looking at furniture with a natural finish, so you can see the grain. There might be a restored historic building in your area, and they might offer tours. Be sure to ask questions if you have the opportunity tour an old home. Some lumber yards will have displays of wood samples finished with various methods.

Good advice, above. Also note that sometimes the best way to identify a wood species is to look at the end grain with a magnifying glass. Wood types that have similar face grain often have very different end grain. You might be able to pry off a piece of trim (for example) and "freshen" up the end with a sharp razor blade so that you can get a good look. Under magnification you will be able to see the pattern of pores and rays, which can be compared with online reference images. I don't know of any one site that has a comprehensive set, but with a little searching you can find images for lots of species. See the links below.

During our last remodeling project, we wanted to have new wood trim made up to match the old. We took a sample to a custom wood fabrication and milling company, and they couldn't tell us for sure what it was. They thought it might be maple. Turns out it was white birch.

Here is a link that might be useful: end-grain images

Thanks for all the great info, tips, etc. I did neglect to mention we live in the NYC metro area, so that might narrow down my search a bit (I don't think the original builders of this house would've gone for an "exotic" wood, but who knows). Lots of great things to look through - thank you so much!