First you need a balanced chemical equation for the reaction.
Next you can plan out your calculation. It will go something like this:
grams of Zn → moles of Zn → moles of ZnI2 → grams of ZnI2
grams of I2 → moles of I2 → moles of ZnI2 → grams of ZnI2
When you do the calculations, you'll start with the 1 gram for each substance, then do the conversions using conversion factors. The g→mol and mol→g conversions come from the molar masses of each substance. The mol→mol conversions come from the coefficients in the balanced equation.
You'll get two answers (and they're usually different), but the correct answer is always the smaller one. The smaller answer comes from the reactant that runs out first while the reaction is taking place; that reactant is called the limiting reactant. You can't get the larger amount (the one from the other reactant), because you don't have enough of the limiting reactant to keep the reaction going. The other reactant is called the excess reactant. There will be some of the excess reactant leftover after the reaction stops.