Additionally, most hydroelectric power plants consist of more than one turbine. They can turn some of them off completely if they need to reduce load.
The other thing power companies do is build additional easy-on plants (typically natural gas turbines) that will be powered up only when needed for peak loads.
Also, wanted to point out that right now in the US and other developed countries, storage isn’t a big issue for solar power. The peak demand for electricity is nearly always on the hottest days (air conditioners need a lot of power), which is happily the same time that solar generation is highest. And, since most of peak electricity is supplied by plants that are only brought on-line during peak demand, adding solar doesn’t require much change to the base load supply.
Now, in the long run, for solar to supply much more of the total, and especially if fossil-fuel heating is phased out, good storage is necessary. But it’s not necessary right now for solar to be valuable and useful.
Many of the power plants remain at a steady output. There is usually one or more plants that are designated as load following plants. These plants have generators that automatically respond to small changes in the frequency of the system. (like a shift from 60hz to 59.9 Hz). Additional load will have a slowing effect on the frequency so the load following plant will respond to a downward frequency shift by outputting more power. Should the load drop it will cause the system frequency to speed up and the load following generator will output less power.