Yeah, there's bluegreen bacteria (cyanobacteria) everywhere. The last cup of water you drank probably had some floating in it. Cyanobacteria don't grow well without an excess of nutrients; so keeping nutrient supplies low (plants don't mind this) will keep alage growth to a minimum. That's accomplished by lots of plants and the lighting and Co2 to keep them growing rapidly and a low fish stocking. Frequent water changes also work; provided your tap water doesn't have any nitrates, phosphorus or potassium in it.
I prefer the plant option, it's less work, looks better, keeps the fish happier and I gain a preverse pride in knowing that I spend a fraction of the time on my tank that other people do and acheive a better result. I've gone 4 months (purchase a nitrAte test if you try this) without a water change, and although alage did grow, the plants held their own against it for a while. Things are still ok thanks to a low fish stocking, but once I get my new DIY canopy and Co2 hooked up things should go well.
I suggest you buy "Ecology of the Planted Aquarium" by Diana Walstad; it's the best money you will EVER spend on fish.