So you have a new horse, everything in the world is right and all is well. But, oh, wait, the horse is green? Hasn't been broken in and is completely untrained? You don't know what to do or where to start. How do I train the horse? What methods do I use? Who do I call? Should I just send the horse to a trainer? AHHHHHHHHHHHHHHHHH!!! You scream in utter despair.

I'm no horse trainer, not at all, I don't even own a horse, but I have read book after book, researched and googled and observed until my eyes melted into goop. While all that is good to do that still does not qualify me as a trainer. BUT. I can give you a few options of different training methods out there, their purpose and how they came to be.......maybe. 

I have never been a very assertive person...like...ever. I have a hard time saying no and a hard time NOT saying yes. It's true. People will ask me to do work, I'll agree..and keep agreeing..and keep agreeing..until I'm so overworked it's not even funny. So, if I can't say no to a human being, I certainly couldn't say no to an animal as big as horse...and I definitely couldn't say no and tell that horse what to do too. I didn't shout, kick, yell, slap and show any kind of harshness at all to the horses. So you can imagined the horses really pushed me around and did what they pleased. I cried, literally cried, many tears. I did actually have injuries, minor, that resulted in blood and there was a heck of a lot of sweat involved too. Yep, blood sweat and tears, the whole package. I was on the brink of quitting, giving up my love for horses because I was convinced I was no good. Then I was introduced to Parelli Natural Horsemanship. It changed the way I looked at horses and introduced me to a new way to train them.

Parelli Natural Horsemanship(explained by wikipedia as that's a lot of typing haha): 

Program

Parelli Natural Horsemanship states its core principle as "Horsemanship can be obtained naturally through communication, understanding and psychology, versus mechanics, fear and intimidation."^[3] Parelli's methods were first publicized by Robert M. Miller in a series of articles in Western Horseman magazine in 1983 and 1984.^[4] In 1993, Parelli published his first book, Natural Horse-Man-Ship, co-authored by Kathy Kadash Swan and with photography by Parelli's first wife, Karen.^[5][a] The Parelli program is now promoted as co-founded by Parelli and his second wife, Linda.^[7]

The Parelli program is offered via courses in Colorado, Florida, Australia and the erted Kingdom^[8] and includes a four-part training program of horsemanship referred to as "The Four Savvys".^[9] The exercises developed by Parelli that emulate these behaviors are referred to as the "7 Games".^[10] The "Parelli Natural Horsemanship University" was approved as a "private occupational school" by the Colorado Department of Higher Education in 2003.^[11] It is listed under the state's Division of Private Occupational Schools as a private, for-profit institution.^[12]

The Four Savvys

"The Four Savvys" are defined by the Parellis as types of play with horses.^[9] Two, Online and Liberty, involve the human on the ground and the horse typically is in a halter with an attached lead rope, but other methods of connection such a flank rope are also used.^{[10][not in citation given]} Liberty play involves a horse who is not physically connected to the human. Instead, the horse is asked to watch the body language of the human as its primary source of information about what they are supposed to be doing. The two riding categories are named Freestyle and Finesse. Freestyle consists of riding with infrequent or no contact with the horse's head or mouth. In finesse, the rider generally keeps close but gentle head/mouth contact and uses communication from body cues developed by practice with freestyle riding to give instructions to the horse about gross motor skill topics such as gait and direction while reserving the reins for discussions regarding refined elements such as bend in the body.^[13]

The 7 Games

Within the four savvys, Parelli Natural Horsemanship teaches the use of the "7 Games" with horses. The Parellis state that these exercises emulate the behaviors that horses engage in with each other.^[10] The first three games are also known as the principal games, as the other four games, called the purpose games, consist of elements of these three games.^[14] The seven games are:

1. Friendly: also known as the confidence game, is designed to demonstrate to the horse that the human and their tools are not a threat and to establish a rapport with the horse.
2. Porcupine: a game of steady pressure that motivates the horse to move away from that pressure to obtain relief.
3. Driving: a game of rhythmic pressure that is used to motivate the horse to move.
4. Yo-yo: a game of "back and forth," which can mean that the horse backs away from the human and returns. Another type of yo-yo game involves the horse speeding up or slowing down.
5. Circling: often compared to longeing the horse, although Parelli asserts that the two are distinctly different. In the Circling Game, it is the horse's responsibility to maintain both the requested gait and direction instead of the human's responsibility to enforce the gait and direction.
6. Sideways: a game where the human causes the horse to move laterally.
7. Squeeze: a game where the human causes the horse to "squeeze" between objects.^[15]

Horsenality

The program uses a concept the Parellis call “horsenality” to explain the behavior of individual horses.^[16] The system adapted parallel concepts for humans derived from the Myers–Briggs Type Indicator,^[17] based on Linda Parelli's study of personality psychology, which she has applied to horses.^[18] Many of the studies supporting the MBTI itself have been criticized as methodologically weak or unscientific.^[19] There are no independent clinical studies examining this theory as applied to horses, and the concept of "horsenality" has thus been dismissed by some critics as "nonsense."^[17]

Parelli is what I use in my approach to any horse I meet. I plan to get certified in Parelli later down the road, after college.

Joining Up(info provided by About.com):

Definition: Join up is a method of bonding with a horse through body language. Body position and eye contact are used to send the horse away from the handler, and then to invite the horse to approach. If the horse does not approach the handler respectfully, it is again sent away from the handler and asked to move out along the fence surrounding the training area, usually a round pen.

The theory behind join up is that the horse will feel segregated from the herd leader (handler) and then act appropriately to be accepted.

Signs of appropriate behavior and successful join up include a lowered head, licking and chewing while walking quietly to the handler. This method was developed by horse trainers looking for more humane ways to train un-handled horses that did not involve violence. It was popularized by horse trainer Monty Roberts.

Some people like to use this method to begin training and working with horses, when the horse joins up with them, they go from there.

DownUnder Horsemanship(as explained by Clinton Anderson):  About Clinton Anderson and Downunder Horsemanship