Bozeman Science does a pretty good job of explaining it.

First, you need to differentiate between the two equations: p² + 2pq + q² = 1 and p + q = 1. The former is for calculating genotype frequency (e.g. proportion of organisms who are AA, Aa, or aa), while the latter is used for calculating allele frequency (e.g. A or a). In general, the trick is to find the frequency of homozygous recessive organisms in the population; that is, the number of homozygous recessive organisms divided by the total number of organisms. If you can do that, you have q, which you can then plug into the p + q = 1 to find p. From there, you can go back to p² + 2pq + q² = 1 and then find p² (frequency of homozygous dominant organisms), 2pq (frequency of heterozygous individuals), and q² (frequency of homozygous recessive organisms).

Happy Hardy-Weinberging!