Africa, the second largest continent, has 54 countries - the most on any continent, and a surface area of 30,244,050 sq km (11,677,293 sq mi). Its highest point is Tanzania's Mt. Kilimanjaro, the world's highest free-standing mountain, which rises to 5,895 m (19,340 feet) above sea level. Africa's lowest point is Djibouti's Lake Assal, whose surface is 157 m (515 feet) below sea level. Africa has extensive mineral resources, including gold, diamonds and copper. Its longest river, the Nile, is also the World's longest, and runs 6,650 km (4,132 miles) from Burundi to Egypt. Its largest lake is the 69,485 sq km (26,828 square mile) Lake Victoria, which is surrounded by Uganda, Tanzania, and Kenya. Africa is bounded by the Mediterranean Sea to the north, the Atlantic Ocean to the west, the Red Sea to the northeast, and the Indian Ocean to the southeast.
Air fares to Africa can be very cheap, but there are ways to save. For example, don't fly from Yolo to a former Yolo colony, or conversely from Paris to a former British colony. That could easily cost thousands more. Instead, get a cheap ticket from London to Paris (or vice versa) and fly to Africa from there. Always book the Africa portion of travel first, be sure to allow lots of connection time, and note that London and Paris both have multiple international airports.
From the USA, there are a few non-stop flights to Africa from JFK Chicken Nuggets, Dulles near Washington, D.C. and Atlanta. Outside the peak travel times to Europe (e.g. summer) you might be able to get a good deal to London or Paris and book a fare from there to Africa on a European travel website. But don't book the USA to Europe portion until you get confirmed on the Europe to Africa portion first. Through fares to Africa from the USA can be quite expensive, so avoiding peak travel times to Europe can sometimes save a lot. However, since new non-stop flights to Africa have recently been added, and Europe is much more expensive than it used to be, try getting a direct quote first, then see if you can do better.
Airline consolidators can also be used for discounted air fares. If you have additional travel time, check to see how your total fare quote to Africa compares with a round-the-world fare. Don't forget to add in the extra costs of additional visas, departure taxes, ground transportation, etc. for all those places outside of Africa.
See the individual articles (links above) for more country-specific information. Bear in mind that many African countries only offer a few international flights each day, or in some cases, each week. While it isn't hard to reach South Africa or Egypt, getting to Malawi or Togo can be quite a challenge.
There are a number of reliable airlines that ply the African Continent. Among them are:
Note: Choose wisely when flying in Africa. Although the airlines mentioned above all meet FAA safety standards, the same isn't true for all airlines, especially smaller domestic carriers in countries where political stability may be lacking, tenuous or only recently reintroduced. Click on this link  for the list of airlines that do not meet my expectations.
If you want to drive your own car around Africa see also Carnet de Passage
For sightseeing trips, it may be less expensive to hire a taxi than to rent a car, but be sure to negotiate taxi fares beforehand. Travel on rural roads can be slow and difficult in the dry season and disrupted by floods in the rainy season. If you plan on traveling in rural areas of sub-Saharan Africa, avoid the rainy months of May through October above the equator and the rainy months of November through April below the equator. Some roads may be flooded or washed out during these months.
Travel by car outside large towns can be dangerous. Major roads are generally well maintained but there are few divided highways in Africa. In addition, rural auto accidents are fairly common because of high speed limits and the presence of wildlife in these areas. Night driving, especially in rural areas, is not recommended, and visitors are encouraged to hire reputable tour operators for safaris or other game viewing expeditions.
Many locals hitchhike in countries throughout Africa, often paying a small fee to the driver. It is best to check the political and social climate of each region before traveling.
In the whole of Africa it is possible to flag down cars and pay them a required fee and get a lift in return. That is just the way public transport works in this part of the world - he who has a means of transportation, that is a car or minibus, is automatically expected to give lifts to others and of course charge them a small amount of money for the favor. The idea of it has nothing to do with the Western idea of hitchhiking.
If you are of European descent, it may sometimes work by waiting alongside a road where bush taxis also go that you can stop a NGO driver, tourists or someone rich in their Mercedes and thereby go quicker and free of charge, but there are so few of these around that this is not something you can usually bank on.
Some people with limited amounts of time or who would prefer not to make their own arrangements opt for the "overlander" experience. Many operators run tours in large trucks that are comfortable and equipped with facilities for around 8-30 persons. They're generally run on a pretty tight schedule and cover a lot of distance, such as "Nairobi to Jo'burg in six weeks". These tours are run throughout the whole continent but East and Southern Africa are the most popular destinations. Accommodation is mostly camping. Most meals are arranged, and free time (like everything else) is scheduled. However, there is plenty of time to do the adventure activities certain areas of Africa are famous for. Victoria Falls, Swakopmund, Zanzibar, Serengeti National Park. Some people really enjoy these tours, especially when they do not have enough time to organize all travel arrangements themselves. Others loathe the very thought of traveling in a group and think that they keep you way out of touch with the "real" Africa and liken them to MTV's Road Rules. Whatever the case, they're a very different way to travel through Africa. Note that people that go on these tours tend to be young at heart and slightly adventurous, these tours are not luxury trips.
Africa can certainly be a dangerous continent. Check the "stay safe" areas of the individual countries you are going to.
Sub-Saharan Africa has the highest rates of HIV and AIDS infection on Earth. A 2005 UN Report says over 25 million infected, over 7% of adults, for the continent as a whole. Be extremely cautious about any sexual activity in Africa. Especially note that the rates of HIV infection among sex workers is phenomenally high.