My website is suddenly slow: where do you look?
"Suddenly" is the most important clue. If a site was fine yesterday and drags today, something changed, and it is almost always one of these things.
An update
A plugin, a theme or a CMS version installed recently. Check the update log first: it is the most common cause and the easiest to undo.
The database
Tables that keep growing — sessions, logs, revisions — slowly make queries heavier, until a tipping point that feels sudden.
Unusual traffic
Bots or a scanner can load your server without your visitor numbers going up. Your statistics will not show it; your server logs will.
An external service
A font, a tracking script or a slow third-party API drags your page down while your server is perfectly fine.
Measure before you fix
First test whether the server is slow or the page is slow. Those are two different problems and they need two different solutions.