To diagnose problems with a boiler, first check to see if it has a screen, as boilers sometimes self-report problems. Check to see if the emergency gas valve is open. Inspect the stopcock to see if gas is flowing into the system. If it isn't, the problem is likely due to a issue with the gas delivery.
It is also worth checking the power supply by making sure the boiler is plugged in properly. Many boilers have lights that turns on when the boiler has power, so if this light doesn't turn on, even if the boiler is plugged in, the problem might be with the electrical outlet.
Check to see if the pilot light is on, and follow the instructions, which are often printed on the boiler itself, to reignite it. Some boilers don't have pilot lights, and most of those have a deblocking button or other reset switch. Try pressing this button to see if it reconnects.
Look at the boiler's controls to make sure the thermostat is set to the On position. If it is, increase the temperature of the system to see if it starts working. If everything seems to be working, but the boiler still doesn't start, the problem might lie with a faulty thermostat, which an expert can repair.