Don't rush right out and buy a telescope. It is strongly recommended that you begin to learn the sky by using your unaided eyes. If you already own a pair of binoculars (no matter what their size), use them to reveal dimmer objects the eyes cannot see. They are easy to use and very portable.
Do attend public stargazing events in your area. Contact your local amateur astronomy organizations.
Read Astronomy Magazine - available by subscription, at newsstands and libraries, and on the web.
Use a red flashlight when you go out to look at the sky to preserve your eye's dark adaptation. At night it takes about 20-30 minutes for the eye to become fully dark adapted. It takes only a fraction of a second exposed to white light to lose it. Red cellophane, red construction paper, etc., may be placed over the end of an ordinary white flashlight. Even a brown paper bag will help some.
Choose a safe place to observe. Tell someone where you are going.
Never observe alone! It is more fun to share the experience with a friend and it is much safer.
Dress extra warm. It gets chilly at night when one is not moving around. Dress in layers; wear long johns, wool sweater, boots, hats and gloves in cool weather.
Be comfortable!!! Lay on a lounge chair or blanket to avoid straining your neck. You will enjoy it much more. A blanket or a sleeping bag may add to your enjoyment.
NEVER LOOK DIRECTLY AT THE SUN with your eyes, binoculars, or through a telescope! Looking at the sun through binoculars or a telescope without a proper solar filter will result in instant and permanent eye damage or blindness!
Acquaint yourself with maps of the sky. There are many good star maps available. (suggested titles)
When you feel you need more than just your eyes, consider buying a pair of binoculars before purchasing a telescope. Ordinary binoculars come in 7x, 8x, and 10x magnifications. The larger the magnification, the more difficult it is to hold them steady without shaking the image. 50 mm objective lenses are recommended for astronomical purposes, e.g., 7x50, 10x50. A pair of binoculars is a good investment since they may also be used for birding, football games, etc.
Join a local astronomy club. There you will meet people who love the sky and are willing to share their knowledge, observing skills and equipment.
Read books (suggested titles) from your local library or bookstore. Start reading children's books and work you way up.
For Telescope Users:
In the beginning, use only your lowest power eyepiece, the eyepiece with the highest number (i.e. 32 mm, or 26 mm). Do NOT attempt to use high power eyepieces (9 mm, 12 mm) or a Barlow Lens. Leave them in the box for now!
If your tripod is the least bit wobbly, suspend a backpack loaded with heavy objects from the underside of the tripod using bungee cords. This will help stabilize it and make a world of difference.
Align your telescope finder during the day. Find some small, distant object in your telescope using the highest numbered eyepiece (lowest magnification) you have (e.g. a light bulb on a distant neighbor's house). Then adjust the finder scope so that the object is positioned at the cross hairs in the finder. Progressively change eyepieces until you get to the lowest numbered eyepiece (highest magnification). Readjust the finder with each eyepiece. On the next clear night, locate the North Star (Polaris) in the finder scope. Be sure your highest number (lowest magnification) eyepiece is installed. Place Polaris in the center of your eyepiece. If necessary, re-adjust the finder. Progressively change eyepieces and readjust the finder until Polaris is in the center of your lowest numbered (highest magnification) eyepiece and on the cross hairs of your finder. Your telescope and finder are now aligned properly and you should be able to locate objects easily.
Consider investing in a finder without magnification such as a Telrad, TeleVue Quick Point, Orion EZ Finder, or a Daisy gun sight which with a little creative adaptation can be mounted on a telescope with double face foam tape or epoxy (it can usually be purchased at Wal-Mart or K-Mart for under $20).
Begin by observing the Moon, planets and the brightest night time stars.
NEVER use a sun filter that attaches to the telescope's eyepiece! Use a special solar filter that attaches at the front end of the telescope. If your older telescope came with a sun filter that attaches at the eyepiece, take a hammer and destroy it immediately so that no one will become blinded by looking at the sun through it.