Now take one small step

That same weight sat at 0.60 with a positive gradient. Increasing the weight would raise the error nearby, so training moves in the opposite direction. The weight becomes 0.58.

Not 0.20, and not 0.59999. A small step opposite the gradient.

The optimizer can update many trainable weights in the same step, each by its own amount. A frozen weight or a weight with a zero gradient does not move. Then the network tries another group of examples and measures the error again.

Training does not test every possible combination or jump straight to a perfect answer. It takes one informed step, checks the result, and repeats.