Honestly I do it by hand and don’t see how this could be fully automated at home. Every clay chip is very slightly different.
After you’ve done a few dozen, you’ll get quick at it and the process becomes intuitive. I use my fingers and hold the chip pretty close to my eyes so I can accurately view the contours.
But it’s almost more of a feel thing. If I had to describe it, I sort of push one edge of the label into an interior edge of the recess so it is lightly attached on one side. If the label is properly sized it should then be easy to slowly let the rest of the label roll down into the recess, and it will fill the space.
If the label does not fit well, some adjustment may be necessary, which is why I don’t run my thumb over it to fully adhere it until I’m sure it’s placed correctly.
Labels tend to get easily ruined if you handle them too much. You can try to lift a misaligned label with the tip of an Xacto knife or similar tool. But you can expect some wastage on a few if you are applying hundreds or thousands of labels, which is why vendors like Gear tend to provide some extra.
For me the slow part is not adhering the labels but peeling them off the backing. I’ve tried many methods for speeding this up, none perfect.