Unfortunately, this isn't entirely accurate or thorough.
Algae can be a problem because you have too much lighting, because you don't have enough CO2 in your system because of high lighting or because nutrients are not in check.
Balance is key. Once you find that balance for your specific tank, you will have very few issues with algae.
The plant establishes itself in water with high levels of dissolved food. When you feed your fish and plants too much, then there's extra food for primitive plants like algae.
It's a slow process, but you can remove it by slowly reducing the amount you feed. In their natural setting, fish and plants are lucky to eat once a week. We need to feed the same way.
I feed fish and plants a little bit a couple of times a week and only what the fish will eat in a minute or two. That way, there's no added nutrients in the water. I have no visible algae in any of my planted tanks.
I also remove and replace half the water in my tanks, so if I feed a little too much, the water change will remove the added food.
Pretty simple, but it takes time. The algae didn't magicially appear overnight, so you can't get rid of it overnight.