To solve the Rubik's Cube , cubers use methods. There are many different ones, but each method consists of steps. In those steps, cubers solve part of the cube, so that in the end the cube is solved.
In order to solve part of the cube in each step, cubers turn the sides certain ways, changing something. This is called an algorithm. Cubers learn algorithms, "alg(s)" for short, to complete different steps.
Methods and algorithms don't just come out of thin air. Cubers have to discover them. When cubers discover new algorithms, they have to test a lot. They have to try different moves to see what they do. Sometimes it takes a long time to discover algorithms, other times it doesn't.