How do plant stems know to grow toward the sun?

They don't, it's built in.

Stems grow toward the sun because that is how the leaves they bear get the energy to produce the sugars they need for food. If they grew the other way they’d be roots. Important, yes, but not what we’re up to today.

Plants contain hormones (special cells release chemicals-hormones-which travel to another part of the organism to cause an effect). Light causes the plant hormone-auxin-to travel to the shadier side of a stem. Only blue, white or ultraviolet light will do, green, yellow or red don’t work. Obviously a pigment is involved to absorb those particular colors.

The auxin causes the plant cells on the shady side to grow somewhat longer. If the cells on the shady side of the stem grow longer while those on the sunny side don’t, then the stem is forced over toward the sun.

Many chemical weed sprays are actually synthetic auxins. When they are sprayed on growing plants they accelerate the growth to the point where the plants grow too fast and die.