While there are rough guides and experience, wood identification is a scientific discipline and involves evaluating characteristics, including microscopic evaluation of end grain.

Certain woods have natural coloring, respond better or poorer to certain stains and finishes. Other than that, I'm not sure why it matters. You have the pieces and they are what they are.

In an antique piece, the most likely candidates are:
- hard maple
- cherry
- walnut
- birch
- poplar (generally finished to look like something else)
- red oak
- white oak
- mahogany

Here is a link that might be useful: book you might find at your library.

"I have several pieces of antique furniture that need to be refinished. How does one tell what kind of wood a piece is made of?"

The finish chosen does not have all that much to do with the type of wood unless you are looking for specific finish styles (like 'pickled oak' say).

Different types of wood can require more steps (like pore filling if a smooth surface is desired) but once again, if the wood does not have open pores it would not need filing.