You paint it and then "weather" it by wiping, rubbing, maybe staining. Your library would have books on different finishes and I bet You Tube does too.
Check out how I did it on furniture in my guest room: https://happydealhappyday.com/7-ways-re-decorate-room-budget/
Vicki: maybe this will help
Here is a great layered weathered look with paint https://arayofsunlight.com/white-farmhouse-tables-with-weathered-wood-tops/
Here's a good tutorial, and the paint she used is literally called "Weathered Wood"