An ounce is 30 ml in home rounding, a centilitre is 10 ml, a dash is about a millilitre, a barspoon five. A "part" is a ratio, not a volume: "2 parts gin, 1 part vermouth" works in any glass while the ratio holds.
Nearly all the classics reduce to a few formulas. The sour: 2 parts spirit, 1 part citrus, 1 part sweet — that is the Daiquiri, the Whiskey Sour and the Margarita. Equal thirds — the Negroni. Spirit plus filler at one to three or four — every highball. Knowing the formula lets you repair a drink: too tart — add syrup, flat — add citrus, weak — add spirit.
Homework: make a 2:1:1 Daiquiri, taste it, then move the syrup half an ounce each way. Find YOUR balance — that is what proportions are for.