There are four ways sulfuric acid can react, these mainly depend on the amount of reactants available, and how concentrated sulfuric acid is. You are not expected to judge which reaction will take place, as they usually all react to a certain extent. If you need to balance an equation, the question will tell you what key product is formed.
H2SO4(aq) + Zn(s) --> ZnSO4(aq) + H2(g), this reaction usually take place in solutions (i.e. not pure or highly concentrated H2SO4)
2H2SO4 + Zn --> ZnSO4 + SO2 + 2H2O, half eqn SO4 2- + 4H+ + 2e- --> SO2 + 2H2O
4H2SO4 + 3Zn --> 3ZnSO4 + S + 4H2O, half eqn SO4 2- + 8H+ + 6e- --> S + 4H2O
5H2SO4 + 4Zn --> 4ZnSO4 + H2S + 4H2O, half eqn SO4 2- + 10H+ + 8e- --> H2S + 4H2O
The above three occur with extremely strong solutions of sulfuric acid. The extent of each reaction depends on the amount of metal available. Note that zinc can be replaced by other metals.