i have used H2O2 for years. It's my best friend when fighting algae. What I do is figure out how much H2O2 the tank can handle, load it up in a syringe, stop my filters, and hit the algae with the H2O2. Then turn off the lights. Wait 15 minutes. Turn on the lights and filters. Repeat as needed (I've done it as much as 2x a day). There's no need for a water change since it breaks down from H2O2 to H2O and O (water and oxygen), both of which are fine. A water change may be in order if you kill a lot of algae since all that algae will break down as ammonia, and your current ammonia/nitrite/nitrate cycle may not be able to handle the large load of ammonia from the dead algae. But if you're only working on a small patch of algae, you should be okay just doing your normal weekly water changes.
I have also had good success with doing the full tank method of H2O2. All that means is that I simply dump the H2O2 into the tank (measured amount, of course). Nothing else. The filters distribute the H2O2 throughout the entire tank, filtration system (hoses, etc) and does its job on algae everywhere. Repeat as necessary. It's probably the simplest method of killing out algae that I know of.
I tend to spot treat whenever there is a thicker clump of algae and do the whole tank treatment when there is a more minor breakout throughout the tank. As you gain experience with algae and H2O2, you'll be able to select the method you prefer for various algae outbreaks.
Quick tidbit: H2O2 has been used by professionals to increase the oxygen level in a tank. It can be helpful in times such as long power outages that knock out your filtration (my power was out for almost 2 weeks after a hurricane came through). It's very safe as long as you don't exceed the recommended amount. It's also super cool to watch it in action when it's killing algae!
