Estimators say they take off the quantities from the plans. The takeoff comes before pricing. A wrong quantity makes every later number wrong.
A door hardware supplier takes off hinges, locks and closers from the door schedule. A concrete sub takes off cubic yards from the foundation plan.
People do takeoff on paper, in a spreadsheet, or on screen with tools such as On-Screen Takeoff and Bluebeam.
Work in a fixed order. Mark what you counted. Record the sheet for each line. Takeoff Tool links every line to the sheet or spec text it came from.