Nothing happens if the delay is under 2 hours.
After 2 hours: the airline has to pay for food and drink, 2 phone calls and a hotel stay (if the delay is overnight), including transport to/from the hotel. Ask for vouchers from the airline.
After 3 hours: If the delay is the fault of the airline*, you are now entitled to compensation. You must claim from the airline.
After 5 hours: You now don’t need to take the flight if you don’t want to. It doesn’t matter whose fault it is. You can ask for a full refund for the flight, plus other flights from the airline on the same booking (if you had more than one). They must also pay to fly you back to the UK if you were abroad. Speak to the airline as soon as you choose not to fly with them.
If you stay on the delayed flight, you can get compensation if the delay is the fault of the airline*
(*note: this does not mean unusual weather or workers going on strike).
Be aware these rules might change now the UK has left the European Union.