Pea soup algae is the oldest form of life, and it will usually show up in new ponds and/or ponds that have had their filtration shut down over the winter. The suspended algae in the pond water is consuming the nutrients that have been converted from fish waste and other organics, like decomposing leaves. Algae needs two things to survive: 1. Sunlight, and 2. Nutrients. Pea soup algae also enjoys an environment with a high pH. Here in Central Illinois, our pH runs in the neighborhood of 9.0. The perfect pH is 7.0, or neutral, but to achieve this, you would have to bring it down artificially, which would mean constant monitoring of existing water and any water added to your pond, either on purpose during a water change, or every time it rains. The fish will adjust to a pH of 9.0, and even though it's not ideal for them, they will tolerate a constant 9.0 pH better than they will tolerate any fluctuation. I have found that it's much easier to combat the pea soup problem with plant coverage.
In a typical garden variety pond, the first line of defense for suspended (or pea soup) algae should be plant coverage. You will need 65% to 75% plant coverage to successfully reduce the amount of sunlight the algae is utilizing. Water lilies and lotus are good for this because they help to shade the water's surface, thus cutting down on the essential sunlight the algae needs to survive. These same plants, as well as other marginals like dwarf cattail and such, will also compete for the same nutrients that the algae is feeding on. Once you have adequate plant coverage, your problem will usually go away overnight, and I mean OVERNIGHT. You will wake up one morning, depressed and skeptical about the unsightly appearance of your pond, go outside expecting disappointment, and be elated to find that the pond has cleared itself of the algae and you can now see clear to the bottom and all of your fish. This is by far the best way to get rid of pea soup algae.
If you're impatient and you can't wait for your plants to grow, there are a variety of products that will help you rid your pond of suspended algae, but I must warn you now, DON'T ever use a product that KILLS the algae in one big mass destruction. If you do this, you will only end up with a bigger algae bloom than what you started with. By killing the algae in one fell swoop, you produce a bunch of dead algae, which falls to the bottom of your pond to decompose into dissolved organics and nutrients. It doesn't take long for these dead algae cells to convert over to organic waste and VAWALA! You have effectively produced even MORE nutrients in your pond water than you had to start out with for your SECOND algae bloom! Additionally, most chemicals (algaecides) that kill algae outright will also either kill your plants, or, at the very least, set them back quite a bit.