The most effective way to shave body hair anywhere--face, legs, pubes, etc.--is with a straight razor freshly sharpened on a barber's strap and deburred on the opposite, leather side.
This takes considerable skill and practice and is really a dying art. There are, however, a few old-time barbers and a handful of folks like me who learned from them who still know how to use a straight razor, so I'd encourage anyone who desires a super-close shave to seek one of these experts out to learn the technique. It has to do with knowing just how to pull the skin back with one hand while using the other to guide the razor at the right angle, pressure, and speed across the area to be shaved, plus getting a quality razor, knowing exactly how to sharpen it, and using good shaving cream and after-shave products.
BUT, that takes considerable time and effort.
So, the second-best way to shave is with a so-called safety razor--they do have the potential to cut you--and knowing how to use it. I like the Schick Quattro and prefer the Nivea for Men Sensitive Gel shaving cream and Sensitive Balm after-shave lotion. I use these same products with the straight razor, too. Disregard the "men" in the name, as the gender-specificity is merely marketing, and they work just as well for women.
It's key to get comfortable in a well-lighted area and allow yourself plenty of time. A rush job is much more likely to lead to nicks and cuts and unfavorable results. You'll usually get better results if someone other than the shavee does the shaving, and it can serve as a great form of foreplay, too.
The first step, if the pubic hairs are longer than about a quarter inch, is to remove them with scissors. A good pair of barber's sheers is best for this. They are not cheap, but they'll last a lifetime if reasonably cared for. A good second choice are bandage sheers--the kind EMTs use to cut your clothes off in an emergency. They have the advantage of blunt blade tips, so you don't have to worry about watching the blade ends to keep from inadvertantly snipping yourself as your eyes focus on the other part of the blade cutting pubic hair. Also, dedicate the sheers, whatever kind they are, for hair-cutting purposes only, and don't use them for anything else like paper or fabric. Cut as much of the pubes with the scissors as you can, and brush out the severed hairs.
The next step is to soften the hairs. The easiest way to do this is to take a hot bath or shower first. Or, make a hot a compress with a hand towel soaked in water as hot as you can tolerate, wring it out, and hold in place for a couple of minutes.