The summary.
START WITH THE PHONE
Most visitors are there, and the constraint forces prioritisation.
If something was unnecessary on mobile, it is probably unnecessary anywhere.
DO NOT HIDE CONTENT ON MOBILE THAT DESKTOP USERS SEE
Search engines and most visitors see only the mobile version.
MAKE TARGETS LARGE AND WELL SPACED
A finger is imprecise and obscures the target. Primary actions low and central are within thumb reach; top corners are not.
BASE LAYOUT CHANGES ON CONTENT, NOT DEVICE SIZES
Resize the window slowly and change the layout where it stops working.
The commonest responsive fault is horizontal scrolling, usually caused by one element with a fixed width.
SHOW THE SAME CONTENT, ARRANGED DIFFERENTLY
Different content per device means two things to maintain and one version search engines see.
TEST IN REAL CONDITIONS
One-handed, walking, outdoors, on mobile data, with interruptions.
That reveals every target too small, every control out of reach, and everything that assumed a calm user at a desk.
PRESERVE STATE
People are interrupted and return. Losing their place loses them.