The lines to follow are the ones at the angle that the little arrow points. Which is ‘down and to the right’ from each side if you put that side on top

pick a junction, follow the line to the left, the top right one and the bottom right one

Ternary plots (aka Triangle plots) have three axes rotated and layered on top of each other. So when you get a point like this:

You read it as 50% of the way up the clay direction:

30% of the way up the sand direction:

20% of the way up the silt direction:

So it is 50% clay, 30% sand, and 20% silt.