PPT Slide
Let f denote the forward rate between one year and two years agreed upon now. The investment will grow to $(1 + S1)(1 + f) at the end of two years.
By no arbitrage principle, these two investments should have the same returns (if otherwise, one can long the higher return investment and sell short the lower return one).
(1 + S1)(1 + f) = (1 + S2)2
This forward rate f1, 2 is implied by the two spot rates S1 and S2.