Can I determine a system's $z$-domain transfer function from its pole-zero plot?
Without knowing specifics (ignoring a proportionality constant we'll call K as inidicated in the more compete answer above).  Note that K does not affect the dynamic behavior of the system, so it may not be of particular interest.

it goes like this...

H(z) is a rational function of the form 
$$H(z) = \frac{(z-Z1)(z-Z2)...(z-Zm)}{(z-P1)(z-P2)...(z-Pn)}$$

where Z1,Z2...Zm are your zero values and P1,P2...Pn are your pole values.

I assume you know the exact values of you're poles and zeros. If you don't, you'll have to determine approximations from the PZP.