In WWII most soldiers had either bolt-action or semi-automatic rifles. In subsequent wars, things like AK-47 and M-16 were introduced. How did it change things?
I would argue that the assault rile did not fundamentally change infantry tactics, it was simply a final stepping stone in the transformation of infantry tactics that had been going on for years.
Before WW1 the infantry had been seen as sharpshooters engaged in long range accurate fire, finishing up with a bayonet charge. Obviously this didn't workout so you see the increased use of the machine gun to suppress the enemy.
Between the wars and WW2 you see the number of heavy and light machine guns increase to give increasingly smaller units the ability to perform suppression. The submachine gun was the ultimate expression of this idea since in close range urban combat it gave a single person a suppressing ability.
In this view the assault rifle was simply a development on existing ideas, giving everyone an automatic weapon for suppression while keeping a combat effective sharpshooting ability.
As other uses have pointed out, it didn't change things very much, but was more an adaptation to a battlefield that had already changed thanks to the increased deadliness of supporting arms.
I just wanted to add some supplementary materials you might be interested in.
The Gun is a pretty exhaustive history of the AK-47 and automatic weapons in general
On Infantry is a very dry study of infantry tactics from late 1890s through the 1970s. It is a bit out of date, but covers the period you are asking about.
There is also FM 3-21.8 which covers the US Army Infantry Platoon and squad organization and fighting style. It would be useful to understand exactly how a modern army expects its units to fight and how it organizes them to do so.