How can I reduce the amount of algae in my fish's tank?

What you want to do is reduce the rate of nutrient accumulation in the tank, and you can do that in a variety of different ways. The cheapest, easiest way to do that in most situations is changing the water. Protein skimming will also eliminate compounds from the water by physically removing them. Even if you have a water filter, you trap things like excess food and fish poop inside of the filter. If you have a system like a protein skimmer, you can physically remove those compounds from your aquarium. The key is exporting nutrients.