A half step is one twelfth of an octave.
Formula for a Half Step
Since an octave has a frequency ratio of 2, a half-step has a frequency ratio of 2^(1/12), or approximately 1.0595.
For example, if the note A has a frequency of 440 Hz, then one half-step up is 440*1.0595 = 466.2 Hz. One half-step down is 440/1.0595 = 415.3 Hz.
(Just like an octave, a half-step interval is a ratio obtained through division, not a difference obtained through subtraction. One octave above 440 Hz is 880 Hz, while one octave below is 220 Hz. The size of the octaves in Hz is different, but the ratio is the same.)
Different "temperaments" actually have slightly different half-steps. See the Wikipedia article Semitone for details.