as someone who has recently stained a fence: what I see is 2 different methods. For all the planks, they used a gold-ish colored stain. You can apply that with a wide (5" or so) stain brush you can buy at the big home improvement stores or ace hardware for like $10. it's really easy, just paint it on until you're satisfied.

The harder part here is stage 2: 3 boards were covered in what looks like gray chalk paint and sanded down. they may have added a little black to some parts of the board, too. 4 boards appear to have been dry brushed in black/dark gray chalk paint. All were sanded unevenly, probably with like 40-60 grit sandpaper, to make it look weathered.

good luck!