updated May 2020
Algae is so prevalent in the hobby that for many, it seems almost inevitable and a natural part of a planted tank. This is not the case. Through thousands of interactions with fellow aquarists, the most common 'root cause' is poor housekeeping (build up of decaying leaves and organic matter) and the second 'mistake' is in under-injecting CO2 (while having strong lighting and growing demanding plants) which result in unhealthy plants- and giving algae, which is very opportunistic, the ideal environment to grow. A detailed exploration of the subject is covered here.
For housekeeping, regular water change (every week, or at the very least every 2 weeks) is key. This removes organic matter and helps reset imbalances that inevitably builds up in the tank's closed ecological system. A handy water-change tool is indispensable. As part of housekeeping, a pair of LONG TWEEZERS and LONG SCISSORS are also necessary to trim and remove dead and decaying leaves. A simple but powerful hack in housekeeping is the use of a TURKEY BASTER to stir up debris before 'vacuuming' the substrate surface as part of my regular water change. This is akin to flossing in preventing tooth decay: simple and hugely effective.
Above: one of the simplest and most effective defence against algae is to plant densely, which immediately creates an environment where the plants easily outcompete algae. Sparsely planted tanks are comparatively much harder to keep algae-free.
Well cycled (biologically matured) tanks are far more resilient to algae and I would recommend good tank cycling before adding livestock (which will contribute to organic waste, the the #1 algae trigger). API QUICKSTART (below) is good to kickstart tank cycling. This reduces cycling time to less than a week even when using ammonia rich substrates such as ADA aquasoil. (still need to do required water changes for first week though). SEACHEM STABILITY works in the same way.
Below is a summary of products I have used or have experienced to a degree that I'm fully comfortable to recommend. If you do buy the products through the Amazon links below, I do earn a small commission (at no extra cost to you) which helps in the running of this website. ~The 2Hr Aquarist