Ranch Riding is the first ranch discipline that became available for the horse-show world a few years back. It has gained incredible popularity and there's a good chance, that you'll see it at your next horse show.
As usual, I'll point you to the APHA (p. 266) and AQHA (p. 129) rulebooks to get familiar with the rules. Most Allbreed shows follow the same rules at their shows.
The purpose of the ranch riding class is to measure the ability of the horse to be a pleasure to ride while performing different ranch tasks. The horse should be well-trained, relaxed, quiet, soft and cadenced at all gaits. The ideal ranch horse will travel with forward movement and demonstrate an obvious lengthening of stride at extended gaits. The horse can be ridden with light contact or on a relatively loose rein, but not shown on a full drape of reins. The overall manners and responsiveness of the ranch riding horse to make timely transitions in a smooth and correct manner, as well as the quality of the movement are of primary considerations. The ideal ranch riding horse should have a natural ranch horse appearance from head to tail in each maneuver.
So what should we get out of this almost direct quotation from the rulebook? (I made a few small changes, so it's easier to read for you, who is not a native English speaker)
Transitions are key! There are a lot of them in Ranch Riding and it'll be an area you want to focus on when preparing your horse for this class. Transitions tell a lot about the balance and the training level of the horse and these are very important qualities of a Ranch Horse.
Movements are important in this class as well. We're really looking for that horse you want to ride all day long, while you're taking care of different tasks on the ranch, so it's of course important, that the horse is nice to sit on and is effective in its movements. "Ground covering" is an expression commonly used when describing a good Ranch horse.
Natural ranch appearance is required. The rulebook describes in details that you are not allowed to use fake tails, hoof polish and braids. The use of breast collar and rear cinch is encouraged but not a requirement. Note, that the rulebook never mentions anything about the rider's outfit though! There are a lot of misconceptions around Ranch-outfits and a lot of exhibitors believe, that you are not allowed to wear colors or that the outfits has to be used and dirty-looking. Let's jump back to the purpose of the class: showing a good working horse. If you ever get the chance to visit a working ranch in the US, you'll find that cowboys take great pride in their outfits and their horse. They will wear a good hat and they will groom their horses. Yes, it would be extremely unpractical to wear blingy jackets or using fake tails at the ranch, but at the end of the day, dress code comes down to practicality and personal preference. You can get inspired by watching videos of Ranch work on YouTube or pictures of exhibitors showing at the World Show. You'll see many different styles, colors and patterns. Ranching culture is also different throughout the United States and so are the outfits.
If you turn the page in your rulebook, you'll find 15 patterns. Show management can either use one of these patterns or draw their own based on the requirements of the class.
Another important rule to keep in mind is, that if you're showing Ranch Riding, you're not allowed to cross-enter to Western Pleasure or Hunter Under Saddle at the same show (Western Pleasure only if you show in Europe). This sparks a lot of conversations, specially on the beginner show level, because exhibitors would like to try a lot of different classes before specializing to a few. It's important to understand, that ranching has an important culture and heritage, that all associations are trying to nurture. A Ranch Horse should be a completely different kind of horse, than an All-Around horse and that's why there's a clear line. In the same time, a lot of small, Allbreed shows allow their exhibitors to cross enter, so they can try all the different classes and find the one that fits them best.
I hope that this gives you an idea of Ranch Riding, the ideas behind it and the areas to focus on.