Determine the working frequency band of unknown RFID chip
Many tags use 125KHz and 13.56MHz. Your likley in these 2 bands. Other UHF and 2.4GHz

If your is a passive tag (most low cost tags, designed to work within a few inches, are passive), for sure and definite answer, I have used Radio Frequency spectrum analyzer with tracking signal generator and 1 to 2 inch diameter, self make loop antenna, 

Scan freq range and gradually bring the tag within 1 to 4 inches. 

The spectrum shows a dip as energy is absorbed by the tag at its working frequency.

The same 'dip principle' can be achieved by dip meter which can be home made with two transistors, one diode and others. Wiki dip meter

  

If have spare tag, take it apart. 13.56MHz has coil of a few to 10 turns.  125KHz has more turns, a few tens typically (number of turns are not absolute, these are just typically figures)

This answered the original poster's question on which frequency.  

Please also note that even if freq is right, different tag use many different 'communication standard' (as other responder pointed out) and both freq and standard need to match for successful operation. If the tag is low-cost type, likely, it uses the most popular standards that many readers can read.  In this case, try buy a reader that can read many standards. Or mail one tag to reader seller and ask they test it, reader seller may have many different readers and they can test to see which one matches your tag.

The name, "Radio Frequency Spectrum Analyzer", may have different meaning by context. I refers to the traditional Radio Frequency test instrument, used by wireless engineer (cell phone, police wireless system, etc.) such as this which cover works 30Hz to a few GHz, covering both 125Khz and 13.56MHz (the most suspected freq for the tag)