What to do, in order.
STEP ONE: MEASURE
Run a speed test on three pages. Note the page size and the largest files.
Test on your phone on mobile data.
STEP TWO: IMAGES
Find your largest images. Resize and compress them.
This alone frequently halves page weight.
STEP THREE: CACHING
Install and configure a caching plugin. Test everything afterwards.
STEP FOUR: PHP VERSION
Check yours. Upgrade if it is old, after backing up and testing.
STEP FIVE: PLUGINS
Audit them. Remove what you cannot justify.
STEP SIX: THIRD-PARTY SCRIPTS
Audit them. Remove what does not earn its place.
STEP SEVEN: DATABASE
Clean it, after backing up.
STEP EIGHT: MEASURE AGAIN
Compare against step one.
WHAT THIS ACHIEVES
For most sites, a substantial improvement in a few hours.
WHAT TO DO AFTERWARDS
Check quarterly, and after any significant change.