There are a couple options.
basically, it is some form of storage, coupled with control of the load.
(example is you can turn off some of the air conditioning when a cloud decreases sunshine. natural coupling)
storage options include pumping air or water, to let pressure or gravity help,
battery storage, or some form of spinning energy storage. (flywheel)
or thermal storage (some plants use reflected solar to heat salts, which can be stored hot for use at night)
the issues, benefits, and limitations all seem to be changing as the cost of technology changes, and the overall long term costs of burning fossil fuels and nukes are better understood.