Wi-Fi, the router and the internet

What the boxes do, how to tell a one-device problem from a whole-house one, the restart order that works, and the one button not to press first.

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The pieces

The modem connects your home to the internet provider's line (cable, fiber or phone line).
The router makes your home network and shares that connection with your devices. Many providers supply one box that is both.
Wi-Fi is the wireless link between a device and the router. "Connected to Wi-Fi" only means you reached the router, not that the router reached the internet.

One device or the whole house?

Check another device, such as a phone on Wi-Fi with mobile data off. If the other device works, the problem is on the first device. If nothing works, look at the router, the modem or the provider.

The restart order

Unplug the power from the modem and the router (or the single combined box).
Wait about 30 seconds.
Plug the modem in first and wait until its lights settle, which can take a few minutes.
Then plug in the router and wait again before testing.

Fixing one device

Make sure Wi-Fi is on and airplane mode is off.
Turn Wi-Fi off and on again, or restart the device.
Forget the network and join it again with the password.
Move closer to the router to rule out weak signal.

Do not reset the router first

The small reset hole on a router returns it to factory settings. That erases your network name and password and any provider settings, and every device in the house will need to be reconnected. It is a last resort, best done with the provider on the phone, never a first step.