The most common causes of Blue Algae
First of all overcrowding of your aquarium and therefore to much waste products, from the fish, in the water. If a tank is rather overcrowded, change the water every week at least for about one third. Notice that this is something you should do in every aquarium, blue algae or not.

Clean the aquarium gravel ( or sand )! On the bottom of the aquarium all the organic waste from dead plants, feeding and so on are collected nicely in and on the gravel, an excellent place for blue algae to develop. In one of my tanks I had a blue Algae problem on the aquarium sand. The water was clean, no overcrowding etc... but the nasty stuff always came back. The tank was inhabited with only large fish, no bottom dwellers to eat the small leftovers. I added a group of 9 Corydoras Sterbai and the aquarium bottom was clean and without blue algae within a few days. You could also try apple snails for this purpose.

Corydoras Sterbai

Things to try to get rid of Blue Algae
If the above did not do the trick you could try the following things, over the years I tried them all with different results. Be sure to remove as much of the stuff as you can before you give them a try.

Bright lightning can stimulate the growth of the cyanobacteria, so an easy thing to try is turn of the lights for about 3 to 4 days. The fish don't mind and the plants can take the darkness for a few days.

Although I'm not that eager to use all kinds of chemicals in my tanks I tried adding phosphate to the aquarium water. It worked, but the algae did come back after treatment.

Stop feeding your fish for a few days, and after that give them only a small percentage of the normal amount. This is one for the long run, don't expect results within a few days. It's usually no problem for the fish to eat less for a few weeks.

Reduce the amount of fish in the tank, you can add them again when the tank is more established.

Things NOT to do when you have a blue algae problem
Don't clean your filter! If you clean the filter you will remove all the 'good' bacteria from the filter substrate, these little guys are very important to get rid of the waste products of the fish.

Buy algae eaters, most of the so called 'algae eaters' don't even eat algae that much, but they surely don't eat the blue one, because it's not an algae but a bacteria.

Buy the algae potions, chemicals etc... from the petstores. If your lucky they will kill them for a few days, and some fish and plants in some cases, but it only cures the symptoms. The blue algae will come back in a few days and because they often kill the whole bacterial environment in the aquarium you are right back where you started.