In this presentation that Rita has done, it shows auxin in action. Basically what is happening is that whilst the sun moves along in the sky and at the same time, auxin is being produced in the tip of the plant. The side where the sun is not shining, is the side of the plant where the auxin travels. Photo-tropism then occurs. The cells in the side of the plant that the auxin is diffusing then starts to elongate. Now, because the cells on the shadier part of the plant are longer than compared to the cells on the sunnier side (of the plant), the stem is then forced to lean over to where the sun is shining.
Credit to Rita for the presentation.