A slow website: where do you start looking?

When a website is slow, what’s your first check?

There’s a big difference between a slow initial response and a page that starts loading quickly but takes ages to finish. Then there are problems that only show up in the admin area or during checkout.

Which tools or checks help you narrow it down before changing hosting? If you’re asking for help with a particular site, include what’s slow, when it started and what changed recently. Please remove anything private from logs before posting them.