Three methods cover nine drinks out of ten. Build — right in the serving glass: ice, pour, one stir (gin & tonic, Cuba Libre). Stir — a gentle 20–30 seconds with a barspoon for clear, spirit-only drinks: Negroni, Martini, Old Fashioned. Shake — 12–15 hard seconds with ice for anything with juice, syrup, cream or egg.
The rule of thumb: if you can see through it — stir; if it's cloudy — shake. Shaking also aerates: a shaken sour is alive and bright, a stirred one flat. And the reverse: a shaken Martini goes cloudy and loses its silk (Bond was wrong).
Homework: make a Daiquiri shaken, then the same one stirred. Compare the texture. From here on you understand the methods instead of memorising them.