Mane pulling is done for several different reasons. The goal is to have a maintained mane that looks and feels natural. This may be to keep a refined look for the jumper ring, or this may be to keep a suitable mane for hunter braids.
Not all manes are braidable. To an extent, I guess they are; but in order to achieve nice, consistent, and uniform hunter braids, manes must be properly prepared. Pulling your horse/pony's mane allows the braider to produce small, consistent, and beautiful braids that are meant to accentuate the horses neck, conformation, and all-over turnout.
I can honestly say that there is not one person on this planet that actually "enjoys" mane pulling. Is there a faster and easier way? Sure. Is it correct? No, it is not. Cut manes that need to braided are extremely painful for the braider, and believe it or not, equally as painful for the horse/pony being braided. Razored manes create messy, fuzzy, and un-uniform braids.
Ideally, a horses mane should be pulled several days before it needs to be braided. If your horse gets braided often, your braider will likely be the one maintaining the mane to their personal liking. It is not fair to the horse/pony to et a large mane pull minutes before receiving tight braids. This creates a raw, itchy, irritated crest and will increase the likelihood of rubbed out braids. If you do not know how, please do not hesitate to speak with your braider.
Start with a nicely combed out mane. You will need a stool and a pulling comb.
Start with very small groups of hair. Grab a few long pieces, tease the rest of the mane away with the pulling comb, and pull the few strands out using your fingers. If you have to wrap the hair around the comb, you are pulling out too much at one time. The goal is to keep the horse comfortable and not "anticipating" the large yank. Bounce around to all areas of the neck to avoid making the horse sore in any given region. It is best to do a couple of sessions over a period of time. If you pull all of the hair out at the same time, the hair will then grow back at the same time - setting you up for yet another massive pulling session in the future.
Maintenance is key. Small sessions often.
Mane pulling after a workout makes the hair come out much easier.
Patience. Some horses tolerate this, while others will not. Sometimes a twitch or sedation is needed.
Dentist coming soon? Jump on the sedation train and pull mane when the dentist is done!
Not sure how to pull or is your horse very difficult? Don't hesitate to call a professional!