The spray bottle is for lubrication, spray a bit on the clay and then spray on the car... The clay should glide across with practically zero friction... keep the clay lubricated as you go along... You'll know youself, if the clay starts sticking or feeling like it grabbing the paint, spray some more lube on it...
The smaller bottle in the pack is a bottle of their cleaner wax... Up to you whether you want to use it to wax the car afterwards...