Roofs are made of many different materials, including, clay and ceramic tiles, shingles, asphalt or composition, foam, metal and more. Today's roofer needs to be very familiar not just with roofing, but with roofing using the material he is working with. A professional flat foam roofer is not necessarily an expert in metal roofing, or vice versa.
In the southwest, we typically see foam flats and clay or ceramic tile roofs, with the occasional composition or metal roof for commercial structures.
New materials are often experimented with or used to enhance the function of the roof. For instance, radiant barrier is a heat shielding that is applied to the underside of the roof, from the attic section, and which reflects much of the heat conducted into your home from the outside.
Your first step is to seek out your roof type, and determine what type of material you are working with. If it is tile, can you get a match for that tile? How much of the tile will need to be reset to maintain roof integrity? Will you need to scrape the old tar paper off and put new tar paper down before proceeding? Is the existing paper brittle or cracked? Roof repair requires answering many of these tough questions, and before you can put together your list of materials and go to the contractor depot, you need to know what you will need.