Observing meteors is one of the simplest forms of astronomy viewing: Just look up on a clear night! Of course, to get the most out of the experience, it helps to observe around one of the major meteor showers:
You'll want to generally face in the direction that the radiant - or place from which the meteors appear to emanate - will be rising. For the Perseids, for example, this will generally be towards the northeast for most North American and European observers. But because the radiant often doesn't rise until after midnight, many of the best meteors - and the peak of the shower - will not occur until after midnight. Meteors seen may be dramatically lower prior to the peak. Not only that, Earth rotates "into the stream" of debris that cause meteor showers to occur after midnight, as the part of Earth facing the particles really doesn't happen until after that time. So although you will see some before midnight, the odds of seeing more go WAY up after midnight.
Also, you won't want to look right at the radiant - look from 30 to 60 degrees away, allowing your eyes to see as much sky as possible. The human eye is designed to pick up movements in low-light conditions, so you will likely see meteors "out of the corner of your eye" quite easily. Enjoy the whole sky view!
Turn off all of your lights, and block as many other stray lights as you can. Some meteors are quite bright, but the majority will be faint. You can see more meteors if you let your eyes more fully dark adapt. Use makeshift shields, set up so your house / building blocks lights, or drive to a better location if possible. The more light you can block / turn off, the more meteors you will see.
Night time can be surprisingly cool compared to the daytime, even in what seems like warmer summer nights. Unless it is a balmy 75F or 80F or higher, it is quite possible you may wish to put on a jacket or long-sleeves. Your body will lose a surprising amount of heat a night, just like the unlit side of the Earth radiates heat into space. You body will too. Keep it warm.
Don't underestimate the power of a comfortable seating / lying arrangement. An Adirondack chair, chaise lounge, blanket on the ground, or however is most comfortable for you - do it. Meteor observing is rarely a 5 or 10 minutes long event. Even in cold weather, with enough clothing and a comfortable chair, you can easily extend your time outside and see more meteors. And if there is snow on the ground? Put a piece of cardboard or wood underneath your feet - that will insulate the bottom of your feet from the cold ground. Try it! It really does work.
Not alcohol - it cools your body temperature, and reduces what your eyes will see. If coffee doesn't bother you, that's an option. But usually a warm drink is best - coffee, hot tea, hot chocolate - anything along those lines to help keep you warm if it gets chilly. Make it beforehand and keep it in an insulated container, if possible. Just be sure to keep it in a spot where you don't have to look away from the sky to reach it!
My wife isn't particularly "into" astronomy. She will view the occasional, "Oh... you HAVE to see this!" type of things that I am excited about, but when it comes to meteor showers, she is definitely "all in." We get to spend some time together, we can talk, see "shooting stars" and share a quiet evening either with each other or with our kids joining us. Granted, she's really only keen on this for the Perseids, when it is warm, but that's better than nothing, right? The great thing about these is that they don't take much of any experience - ANYONE can see a meteor streaking across the sky. It takes experience to see the fainter, shorter ones, but few miss the bright bolides when they flash overhead! Share it - it's a great way to share the sky and some time together.
Not everyone does this, but if you are more data-driven and science-minded, you may wish to record your meteor observations. This works best with two or more people working together, that way at least one can always keep their eyes on the sky (!) and not miss any. Record the date, time and location - you never know, although most meteors are sand or small-gravel sized, occasional large ones may make it to the surface (though they may not be from the meteor shower debris). But it never hurts to record all you saw anyway - knowing how intense a meteor shower was one year compared to another can be useful information.
Whether you get into serious data records or just go outside and enjoy the flashes of light in our upper atmosphere, enjoy yourself and have fun!