Most of the purebred Jersey people I know go cold turkey IF the cow is producing 2 gallons or less per day, and has no history of mastitis. In that case they just stop milking and yes, the cow's udder will be huge for a couple of days, and yes, she will holler, but it's all about supply and demand, and she'll stop producing milk and reabsorb what's in her udder over time. Oh, and they also stop feeding grain and supplements (including alfalfa), and just feed grass hay.
If the cow is producing more than 2 gallons a day, what they normally do is milk every other day for a week or so, then every third day, getting the production to slow down, but completely emptying her udder periodically (which also helps to avoid mastitis), until she's down to less than 2 gallons a day, then stop cold turkey.
I usually milk my 3/4 Jersey until she's down to a gallon a day, or two months before calving if she's been rebred that year, and I stop cold turkey, BUT I always use a dry treatment udder infusion because my girl DOES have a history of mastitis. She's been clear for the last 3 or 4 years, but it's because I judiciously use the dry treatment and then don't touch her udder again, except out in the pasture. If she's in the barn, or anywhere near the milking stanchion, and I put hands on her udder to check progress, she lets down, and I don't want her to do that if I'm drying her off. Mostly I try to just LOOK and see how things are going. I don't feed grain, so I don't have to do anything feed-wise, but they do have pasture, however I usually calve in the fall, so when I'm drying the girls off, the pasture is winding down and they're getting hay anyway.
My 3/8 Jersey 5/8 beef cow I just stop milking when I decide to dry her off. She's usually on her way to doing it herself, since her job is to make milk for her calf. I usually get a few months of milk after weaning, but not much more. That's OK, by then it's time to dry her off anyway.
There are a lot of different ways to dry a cow off, but as long as she doesn't end up with mastitis, any of them will work. Whichever works best for you is the best way. For me, it's cold turkey, but mine isn't a full dairy cow, AND she's getting up there in age, so not a huge producer (4 to 5 gallons a day at peak now). She hollers at me for a day or two, leaks milk about the same amount of time, then starts reducing. It usually takes about a month before her udder is dry again.