Step 1: Buy a Red Torch
It takes between 40 minutes and an hour for your eyes to become fully adapted to seeing in the dark, but even astronomers need a little light to read a chart or tend to equipment. Unfortunately, any exposure to bright lights will instantly ruin your eye's acclimatization to the dark.
The solution to this problem is to use a red light that won't affect your ability to see in the dark. It's best to resist using a rear bicycle light as bright red lights can be just as bad as any other color. A better idea is to buy a purpose-built red torch, just for astronomers.
Step 2: Buy a Planisphere OR Download an App!
Along with a red torch, the other item most astronomers have is a planisphere. These are very versatile star charts made of plastic that show you the night sky from your location, at any time of year. Some will even show you how to locate the planets. They are cheap and can be bought from most book shops.
Alternatively, there are a vast range of products online to help out. Internet applications and computer software are great but hard to use in the field, so a better option if you have a smartphone is to download an app. For the iPhone, "StarWalk" is by far the best application in my opinion.
Step 3: Subscribe to an Astronomy Magazine
There is no better way to keep up to date with what's going on in the world of astronomy than subscribing to an astronomy magazine. Most countries have at least one or two good ones dedicated to the subject. Inside the covers, you will find news, equipment reviews, classified adverts and even monthly sky charts.
Be warned though, the monthly sky charts will be specific to the country of origin of the magazine. For the beginner, "Astronomy" is great in the US, and "Astronomy Now" in the UK. For more experienced astronomers, "Sky and Telescope" has more in-depth detail.
Step 4: Join Your Local Astronomical Club or Society
Whether you intend to stick with casual stargazing or want to get more involved, a great and very enjoyable way to enhance your new hobby is to seek out your local astronomical society.
These are excellent places to go for advice and help, and eventually you'll find that observing with your new-found friends makes your observing sessions much more enjoyable. You will more than likely have the opportunity to try different types of telescopes so you can make an informed decision before you buy your own.
Step 5: Get Outside and Start Observing
Now it's time for the most exciting bit: Get outside and start learning your way around the night sky. You will be amazed what you can see; those bright stars that aren't on your planisphere are probably planets and on your first night under the stars you may have already spotted satellites, meteorites and the occasional passing aircraft. Time spent now familiarizing yourself with the sky will make your future enjoyment of the Universe much easier.
Step 6: Consider Future Equipment Purchases
Eventually you will want to see more and the only solution is to make that all-important purchase and buy yourself a pair of binoculars or even a telescope. The only words of advice here are to take your time and make sure you spend wisely. Time spent now learning your way around the sky and seeing what equipment is available, and hopefully trying it out at your local society, will be very well spent.