Where did you purchase the wig? Sometimes there IS no way to tell, especially if you picked it up somewhere random. Typically wigs you get from Amphigory, Cosplay.com, and some E-bay sellers will be nice and high quality (and those sellers should advertise it!). I guarantee you that if you found your wig in a local store (even Wizard's Chest), it won't be high enough quality to take a good dye.
Halloween wigs (the really awful frizzy ones purchases around Halloween) are pretty much the worst quality you can get.
What does the bag say the wig's name is? Most good quality wigs will have names like Ashley 850, Perfect, Cher 951, or something like that, so you can always google the name and see what comes up. If the name is simply "vampire wig" or "cheerleading wig" or something, that's another indication of the dreaded Halloween Wig.
Hope that helps!