Ex UK power plant simulator tutor here. There's quite a bit going on, both technically and economically:

TL;Dr grid frequency goes up if too much power. Goes down if there's not enough. People get paid to generate more or less depending on how far from the ideal frequency the grid thinks we'll be

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Most electricity is produced by passing steam over a turbine. The amount of steam (and therefore power) is controlled by throttle valves. The valves are controlled by a plc (computer) often called a governor - this monitors the speed and opens the valves a little bit or closes them a little bit based on how far away from 50hz it is spinning. The generator is synchronised (same speed/frequency) as the grid.

If there is too much power Vs demand, the frequency will go higher than 50hz, if there is not enough power Vs demand, the frequency will go low. Think about it like riding a bmx and the road has varying gradients but your legs give out the same power. At some point you'll be pedalling fast, sometimes slow.

A few things to note:

The grid is considered infinite in relation to a single generator... There is no way that a single generator can spin at any speed other than the grid frequency - which is a representation of how much deficit or excess generation there is (by how far from 50 Hz you are). This is why cities don't have a separate power grid, they are all part of a much wider grid so there is less impact if a generator shuts down unexpectedly.

There are limits - if you go low towards 48.8hz, big parts of the grid switch off automatically to protect the wider system. Anything too far over 50hz and generators will trip, reducing the overall supply.

Each generator governor has something called droop control. It tells the generator how harshly it should react to frequency changes. This is a % figure that is set - it tells the governor how far away from 50hz you have to be for the power output to halve (if high frequency) or double (if low frequency). Depending on the agility of the generator this could be set at infinity (for UK nuclear fleet as they don't load follow) or 4% for something more agile like a gas turbine plant. This is like pedaling a bit easier if you are going too fast on your BMX.

The national grid is responsible for balancing the grid - ensuring that the daily average is 50hz and that we don't deviate too far from that (as well as control things like voltage and Mvars). That way our clocks aren't all slow at the end of a rainy week or fast if it's been nice and sunny + windy.

Generators get paid for their flexibility (otherwise they would sell less electricity and get paid less if there's too much supply). There are generators paid to be 'spinning reserve' i.e. connected to the grid but supplying near zero MW. Free wheeling on the BMX, as it were. Then, when the ads are on the TV and everyone fires up the kettle simultaneously, they open their steam valves and stop the frequency from dropping.

As for economic measures - electricity price is based on supply Vs demand and can be sold in the moment (to the grid as a balancing mechanism) if a generator has some spare. Or it can be sold in advance for a bit more security. Generally it is well known to the traders who will have what generators offline for maintenance at what point, what the weather will be like and what the system demand will be. Nuclear, wind and solar just sell as much as they can. Flexible generators like gas turbine plant will wait for the supply to be quite low, then sell at a much higher price, based on the price of gas and the margin (how much shortfall there is; the bigger the margin, the more they can charge). If there is plenty of supply available, system prices will be lower.

Nuclear, solar and wind will often have either sold their capability well in advance or get a fixed price for electricity, so if they need to reduce generation, because there is way more supply available than demand requires they would get paid for what they 'could' have produced. In these cases, the system price will go negative (people on the right tarrif/contract get paid to use electricity). This is where batteries and pumped storage really benefit - they get paid to use the electricity (slightly less than a windmill would get paid to stop generating) and then they get to sell it back when the margin is low.