There's a lot of threads here about "how to fix the world" or some variation, but I feel like that is a bad approach. Instead of fixing the whole wide world, let's up and fix just a small (or not so small) part of it first - Africa. I'll start with a geopolitical explanation of Africa's woes, and my suggestions for how to correct them.
First, Africa can be divided into roughly six parts, separated by natural barriers that prevent much trade or cultural exchange.
In the north, most settlements are around the Mediterranean Sea. This region has always been rather prosperous due to its ties to Europe and the Silk Road. I don't even really consider it in this discussion, mostly because the region has closer ties to the Middle East and is somewhere between the developing world and the first world when it comes to things like literacy rates and available food. In other words, whatever issues the region faces, they will resolve themselves in the coming years.
The North is separated from the rest of the continent by a vast desert - the Sahara. The Sahara is basically an effective no-man's land that prevents much interaction between the north and the rest of the continent.
The second region, the Horn of Africa and East Africa, is one of the most volatile regions on the planet. The Horn's wealth arises both from trade and oil deposits, but that is also where the region's problems begin. Being so reliant on trade routes has also created a great "melting pot" in the region (minus the melting), where animists, christians, and muslims all clash. The region has much potential, if only the ethnic clashes could end.
The third region,
The Heart of Darkness
Congo river basin, consists of the Congo rainforest. The Congo river is the only real method of transporation and communication in the region, and the thick forest effectively isolates the rest of Africa from the region outside of coastal trade. Crops are also difficult to grow here.
The fourth region is the savannah that grows south of the Congo. This region has permanent access to water due to the Zambezi river, mineral wealth, and fertile farmland.
The fifth region, south of the fourth and separated from it by the Kalahari desert, is South Africa. South Africa is considered a first-world nation, and thus not part of this discussion.
The final region, West Africa, consists of the Niger River basin.
With that out of the way, here is what I believe is Africa's main problem: political boundaries do not reflect physical or cultural realities.
For starters, the entire Niger basin would be better off if it was one large country based upon the Niger river - not 14! The same story applies to the Congo and the Zambezi. Fortunately, all four of these regions could be united relatively easily - they share similar cultural traditions and laws, and at least in one case - the Niger river - there were strong, unified nations there in the past (the Songhai & Mali). While this unification might be achieved peacefully, perhaps by initiatives like a common currency, it most likely will require strong military leaders willing to subject these nations into a cohesive empire.
The problem is much more complex in East Africa, because many cultures all claim to be the legitimate rulers in the area. Frankly there will always be strife in the region until either one side finally wins out or religion's influence wanes. The first is much more likely than the second, and is actually happening now - Muslims are continuing Mohamed's conquests across the Horn, and will probably displace if not outright eliminate the christians and animists in the region in the coming decades. Once that is accomplished the region will finally know peace.
In conclusion, we should allow African nations to wage war with one another, until they have finally fixed their borders the way they like them. It might sound cruel, but ultimately it will end more suffering than prolonging civil and economic strife based on a system that is not in balance.