A slow phone: fixes to try, in order
Start at the top. Most slow phones are fixed by the first three steps.

1. Restart it
A restart clears memory and stops stuck background processes. If you never switch your phone off, do this once a week.
2. Free up storage
A nearly full phone is a slow phone. Get at least 10% free: see freeing up storage.
3. Update the system and apps
Settings → System → Software update (Android) or Settings → General → Software Update (iPhone). Then update apps in the Play Store or App Store. Updates fix bugs that cause slowdowns and battery drain.
4. Find the app that misbehaves
If the phone slowed down suddenly, think about what you installed recently. Uninstall it and see. Check the battery usage list too (Settings → Battery): an app using lots of battery is usually using lots of processor time as well.
5. Fewer widgets, simpler animations
Live widgets and wallpapers use memory. On Android, Developer options let you reduce animation scales to 0.5×, which makes the phone feel faster. On iPhone, Settings → Accessibility → Motion → Reduce Motion does something similar.
6. Check the battery
When a battery is worn, phones slow the processor down to avoid sudden shutdowns. If battery health is below about 80%, a new battery can make an old phone feel new again. See battery life.
7. Factory reset (last resort)
A reset wipes everything and reinstalls the system cleanly. Back up first, check that you know your Google or Apple account password, then: Settings → System → Reset options (Android) or Settings → General → Transfer or Reset iPhone.
When it's simply old
Phones that no longer get system updates become slower with new app versions and also less secure. Check how long your maker promises updates: several Android makers now promise five to seven years, and Apple typically supports iPhones for six years or more.