Finding the right balance is a challenge. The light, nutrients and CO2 need to change at the same rate or algae will take over. It is good to get the plants going strong so that they outcompete the algae. They can best do this when the above are unlimiting however the plants will take longer to adjust to changing levels of light/CO2 and nutrients so it can take 2 to 3 weeks before they really start to grow fast enough to take over from the algae. In the mean time you can take the plants out and bleach dip them (1:20 plain bleach for 10 minutes, rinse very well and then plant them again) however the severely algae-affected leaves will be permanently damaged so it is best to remove them.
Some of the very best running planted tanks have a lot of light and a LOT of plants that are well established. There also should be a lot of fish in there to provide all the nutrients and few water changes or filter cleans. The anaerobic areas of the filter will produce CO2, as will the fish. With occasional trace supplementation, these types of tanks can run well with no algae for years. The key is balance. Once we start adding extra CO2, the plants have an increased nutrient requirement, and vice versa. The more we add, the higher the maintenance requirements become. Once we start adding artificial fertilisers, we need to increase water changes in order to keep the tank in balance and prevent algae issues.