Entropy is a measure of the disorder in a system. Solids are more ordered, because, well, they're pretty much fixed, whereas liquids are more disordered because molecules move over each other, and gases are even more disordered because they're all over the place. So, gases have the highest entropy, and solids have the lowest entropy, although the entropy value will vary from compound to compound.
Generally: if there are more gaseous molecules in the products of a reaction than there are in the reactants, entropy has increased, and if there are less, then it has decreased.
If a solid melts into a liquid, or dissolves in a liquid, then there has also been an increase in entropy.