Fine quality and scarce antique maps are a sound financial investment although this is not the right reason for wishing to collect old maps. It is easy to start collecting. First read a general cartographic reference book or two and visit with a reputable antiquarian map dealer. Ask for that dealer's catalog or list. Try to determine some idea as to what types of maps you wish to collect based on what appeals to you.
Some collectors choose to concentrate geographically.
Others may collect only world maps, celestial or sea charts, miniature maps, city views, etc. Still others concentrate on the maps by the most noted cartographers, such as Ortelius, Mercator, Hondius, Blaeu, Speed, and others. Above right is a celestial star chart by Dopplemayr published by Homann in the 1740's. Below left is a 1659 sea chart of the Pacific by the Dutch cartographer Jansson. An finally below right is a late 19th century view of California's Yosemite Falls.