How do I balance:
1. nitric acid and sulfur react to produce nitrogen dioxide, sulfuric acid, and water.
2. phosphorous, nitric acid , and water react to produce nitrogen monoxide and phosphoric acid.

Like this:

HNO_3 + S \rightarrow NO_2 + H_2SO_4 + H_2O

Count the number of each element on each side, so that there is the same number of them on each side. This gives you:

6HNO_3 + S \rightarrow 6NO_2 + H_2SO_4 + 2H_2O

And, for the second one, it's strange... I always come up with one extra oxygen on the right hand side... maybe the question was phosphorous acid instead of phosphoric acid:

P + HNO_3 + H_2O \rightarrow NO + H_3PO_3