Ah, yes, vibrators. Invented in the Victorian era as a medical device (because back then they thought women got mental problems if they didn't orgasm enough, but it never occurred to them that the solution might have been to get their husbands to learn better sex. Ahem), the "humble" vibrator is the most popular and best known sex toy in the world. Even people who know nothing about sex toys and would be ashamed to admit to owning one know about (and likely, in the case of women own) vibrators.
But what is the best way to actually use one? Is it a no brainer...not always. Women are taught to be ashamed of sex, masturbation, and their own bodies, so it's not surprising most would flail around when it comes to using a toy.
Vibrators are most often used for clitoral stimulation. G-spot vibrators also provide vaginal action, and there are some vibrators designed entirely for vaginal use. Which you pick should depend on your knowledge of your body - but most women find it easier to get a good orgasm from clitoral stimulation rather than from penetration. Also, as many women are uncomfortable with insertion, if you are getting a vibrator for the first time, you should probably stick to the external/clitoral type.
Get used to the vibrator before using it - try it on your hand and go through the various settings. If you aren't used to using a vibrator, heavy settings might be too intense. You should always start with the lowest speed, and if that's too much, keep your underpants on or try through a towel. If you're feeling anxious, then back off - it won't help you achieve orgasm. And remember - many women who have never achieved orgasm do have their first one with a vibrator. Oh, and start with some manual stimulation before adding the toy - you will get a better feel if you're already somewhat aroused.
Definitely use lube - including for clitoral touch (it makes the toy move more smoothly). Never use a silicone-based lube on a silicone vibrator, though - they can react with each other and damage your expensive purchase. And bear in mind every woman is different. The best way to use a vibrator, ultimately, is the way which works best for you.