The basic symbol is a tub, with sloping sides, with waves of water in it.

Inside the water is written the temperature it is to be washed at (in Celsius, of course): just the digits, not the °C symbol. The temperature scale may be (was formerly?) also indicated by a range of dots.

Below the tub is a sign for whatever the technical term in laundry circles is for how vigorously you agitate the stuff, I suppose: nothing for "wash as cotton", one bar for "wash as synthetic", two bars for "wash as wool".

Tumble dry
The basic symbol is a circle inscribed within a square.

The heat may be indicated by a range of dots.

Alternatives to tumble drying are indicated by other symbols inside squares: a sag at the top means "line dry", three vertical strokes means "drip dry", one horizontal stroke means "dry flat", shading slashes in one corner mean "dry in shade".

Dry cleaning
The basic symbol is a circle.

The letter inside it indicates the solvent. F = petroleum solvent only; A = any; P = any except trichloroethylene.

The basic symbol is a triangle.
The basic symbol is a stylized iron.

Inside its body is a number of dots, 1 = cool, 2 = warm, 3 = hot.

A diagonal cross through any basic symbol means not to do it.

I suppose these are international standards. I started by copying them down from the walls of my launderette (even noding addicts have to do the laundry very occasionally), and have confirmed on an American website that essentially the same ones are used there. These were adopted in Britain in autumn 1997, with changes including the use of temperature numbers instead of dots.

Node Your Laundry