This depends largely on what kind of showing you are doing.
What do the judge's look for? Judges are looking for a pleasant picture, a well behaved horse that is easily controlled on a loose rein (loose but you still have contact with your mouth). You need to make the horse look easy and wonderful to ride.
What are you judged on?
Your ability to do up-down/down-up transitions smoothly, Walk to Canter, Canter to Walk, Walk to Trot, Trot to Canter, Canter to Trot. You should know your leads and diagonals. Like I said, loose rein is good but you still need contact with your horses mouth.
What should your horse particularly look like, such as braiding, etc? At a rated show Braiding the mane is a must, tail is only necessary if you are doing A or above. Your horse should be well groomed, polished hoofs, shining coat, the picture of health. Your tack should be spotless and so should you.
What should you wear? A Hunt Coat, any color should do, a matching shirt, breeches in Tan or Khaki, tall field boots, black gloves, an ASTM Helmet, hairnet.
What exactly should the horse know how to do? Walk, Trot, Canter, smooth transitions between all of those. Your horse should go relaxed on a loose rein. Being able to stop square is also desirable.
What do the judge's look for? Same as Rated
What are you judged on? Same as Rated
What should your horse particularly look like, such as braiding, etc? No need to braid for a Non-Rated/Schooling show but your horse should still look amazing. I feel its rude to show in front of a judge and look like you just rolled out of the barn on your trail riding day.
What should you wear? Personally I wear exactly what I would wear to an un-rated show, sometimes minus the Hunt Coat if it is a particularly hot day. A clean pair of breeches and a nice clean polo, clean jod boots and clean half chaps are also exceptable. I have seen people show in just tank tops of jeans before but I was offended that they wouldn't try and look their best.
What exactly should the horse know how to do? Exactly the same as a rated show but you don't necessarily need to be as polished on your transitions.