Maps are the basic tools of geography. They enable us to depict spatial phenomenon on paper. There are conventions used in cartography which allow a map to be read efficiently and quickly.
A good map will have a legend or key which will show the user what different symbols mean. For instance, a square with a flag on top usually represents a school and roads are represented by a variety of widths and combinations of lines. Often a dashed line represents a border. Note, however, that map symbols used in the United States are often used for different things in other countries. The symbol for a secondary highway on a USGS Topographic map is equivalent to a railroad in Switzerland. Make sure to read the legend and you'll understand the symbols.
Every map is a representation of a larger portion of the earth. Read the feature about scale to learn more about how to determine the distance on earth represented on the map.
Without a north arrow, it is difficult to determine the orientation of a map. With a north arrow (pointing in the correct direction), a user can determine direction. Some maps, such as topographic maps, will point to "true north" (the north pole) and to magnetic north (where your compass points, to northern Canada). Usually, you won't see something quite as detailed as a compass rose but a map does need to provide orientation.
A neatline is the border of a map. It helps to define the edge of the map area and obviously keeps things looking "neat."
Since the map is a flat representation of the curved surface of the earth, all maps are inherently inaccurate. There are a variety of projections which have been formulated for different uses.
A map's title provides important clues about the cartographer's intentions and goals. You can hope to expect entirely different information on a map titled "Unemployment in Jefferson County" versus "Topography of Mount St. Helens."
Color appears so often on maps that we often take it for granted that mountains are brown and rivers are blue. Just as there are many types of color maps, there are also many different color schemes used by cartographers. The map user should look to the legend for an explanation of colors on a map.
Our expectations of colors on a map leads to some problems when it is used for elevation. Elevation is often represented as a sequence of dark greens (low elevation or even below sea level) to browns (hills) to white or gray (highest elevation). Since many people associate green with a fertile region, many map users will see lower elevations, which may be deserts, and assume those areas are filled with lush vegetation. Also, people may see the reds and browns of mountains and assume that they are barren, Grand Canyon-type landscapes of desolation but the mountains may be forested and covered in brush.
Additionally, as water always appears bright blue on a map, the user is often inclined to visualize any water on a map as pristine and clear blue - even though it might be entirely different color due to pollution.
I also encourage anyone interested in maps to read How To Lie With Maps, by Mark Monmonier, it's a great book.