Looks like you unsnap the side buckle and then slip the head through the front loop putting the legs on each side of the bottom strip that holds the 2 loops together. Then bring the bottom loop with the buckle around the chest of your dog and snap it shut.
You will probably need to tighten the neck loop to fit better or it might slip off if your baby steps out of it.
We use the step in harnesses that fit like a bra and snap with one side buckle on the back.