"I do not want to miss a good chance of getting us a slice of this magnificent African cake." -King Leopold of Belgium (1835 - 1909)
The Scramble for Africa takes place in the 1870s. This is a guide to get the most out it and leave the least to your competitors. It can be applied to any nation but is most relevant for European and North American nations. A nation needs to be at least a secondary power to get colonization points. A nation have a base of 100 and gets more from naval bases and fleets. Therefore, one needs to invest in a strong navy. More info on the mechanics of colonization can be found here: Colonization
Preparations 1836-1869
Research and Colonial points
If one does not start off as a secondary power, this must be prioritized right away. At least 16th position should be safe by 1870 as the country will be unable to make any further colonial investments if it slips to 17th or worse.
Build up research. Encourage clergymen and invest in education. A nation needs three inventions, which lowers the minimum colonizable life rating:
- Prophylaxis against Malaria, from Medicine (Industry / Chemistry and Electricity)
- Mission to Civilize, from State & Government (Culture / Political Thought)
- Colonial Negotiations, from Breech-Loaded Rifles (Army / Light Armament)
The last one has no chance of being invented without certain techs that unlock in 1870 (unless another GP or neighbour gets it first) and marks the beginning of the scramble. The techs are:
- Machine Guns (Army / Light Armament)
- Economic Responsibility (Commerce / Market Functionality)
- Naval Logistics (Navy / Naval Science)
Having researched one of these techs will give a 25% chance of inventing it per month. Ideally you will be the first nation to research one of these techs and thus be the first nation that begins to colonize Africa. A nation can save up one year's worth of research points, so it is advisable to stop researching in early 1869 and stack up research points for the new tech. In any case, to stand a chance of competing in the race it is imperative to have State & Government and Breech-Loaded Rifles by 1870 so that the inventions are available. As to the choice of which of these techs to take, most players go for Machine Guns since it gives combat bonuses, but if your country's research administration has a penalty to army research (e.g. the USA's Business Schools & Tycoon Capitalism), and especially if you're heavily into the diplomatic influence game, then Economic Responsibility might be better.
Getting a foot in the door
At least one province in Africa is needed as a foothold, the more the better. 
Denmark has a single province in Ghana, which can be taken easily. 
Oman also has colonies in 
Zanzibar and other parts of Eastern Africa. Otherwise 
Zulu, 
Sokoto, 
Ethiopia or the Boer states (such as 
Transvaal) can be annexed. If one is a Great Power, it may also be possible to sphere Egypt and build the Suez Canal, which will grant Suez. This can be helpful to supplement other starting points and colonize Somaliland. It is NOT a good idea to start the scramble from the North African nations.
One needs to invest in a big navy and many naval bases. Therefore, it is advised to research the Naval Doctrine line, which unlocks more advanced naval bases. One might also need to conquer coast provinces to make it possible to get a bigger navy. Landlocked countries should of course annex at least one coastal province but again, the more the better. Ironclads are the most effective ship to build, as they have the best cost to colonial points ratio, and being heavy ships they also increase military score. (Battleships are better, but not available until too late, and take too long to build.) The tech which allows them can be researched in 1860; once it is researched, the best strategy is to build as many as your supplies can maintain. They can only be built in level 3 Naval Bases, which are unlocked by the Raider Group Doctrine technology that becomes available in 1855. Remember that a naval base takes 3 years to build per level, so make sure your home bases (where you'll build your heavy ships) are in order well in advance.
Around 1870 one should ideally have at least 600-1200 free colonization points, but it goes without saying that the more the better.
The most valuable parts - and the least valuable
The most valuable parts in Africa are as follows:
- The coast south of Sokoto (Yoruba States, Benin, and Niger Delta). Huge population and lots of rubber (also some coal and fish) makes it the single most important area to colonize.
- Uganda, Kenya and the horn of Africa. A big population and relatively good crops makes it the second most important area.
- Congo is also one of the richest states.
- Around lake Victoria and lake Malawi.
The least valuable parts of Africa are Sahara and the Libyan Desert. It is no surprise that deserts is not valuable, but one should really avoid them.
Outside of Africa there are a number of states that become available for colonization with Colonial Negotiations. The most accessible are eastern New Guinea, the uncolonized parts of Borneo, and most of the Pacific islands other than Hawaii. Most of these aren't nearly as valuable as Africa (Borneo gets oil in the late game) but to compensate there is typically slightly less competition.
In general you can use the RGO and population density screen overlays, to analyse which parts are the best to colonize.
The beginning of the scramble
The start of 1870 is a very hectic period. Ideally the player is the first nation to invent Colonial Negotiations and get a few months' head start. A great power nation inventing colonial negotiations makes it very likely (10% chance per month, plus a further 10% per month for neighbors) to invent it, so the other nations will follow shortly after. A nation can only colonize a province if they control a province which is either adjacent or has a naval base within 150 naval range. Therefore, one can 'cut off' other nations. E.g. if one colonizes both North Cameroon and Yoruba States, all the provinces between them should be secure. Make sure to cut off the others from colonizing the very rich parts of Africa. Focus on coastlines, as well as inland states that can cut off competitors.
It is advised that one starts off in eastern Africa south of Sokoto and thus cuts off 
United Kingdom, 
France, 
Netherlands and Denmark which have colonies in Ghana. Then one should move northeast until one reaches Ethiopia. From there colonize Horn of Africa to make it impossible to be disturbed from that angle. Then move south until one meets the British or Portuguese that can colonize from 
South Africa and Mozambique. One should be able to secure the Gold Coast, Cameroon, Horn of Africa, Kenya, Uganda, Malawi and down to 
Southern Rhodesia without being challenged.
What you want to avoid - and what you want the other nations to do
Do not by any means begin to colonize Sahara. When one cuts off the competitors at Sokoto, one forces the others to spend time and colonization points on the bare desert.
One can also abandon a colony if a competitor begins on the province at the same time. The time spent can be years that could be used on colonizing other provinces. If one gets a head start and can quickly beat the other nation, then it is better to stay and take the province.
If you've already got some colonies going, it may be advantageous to temporarily contest an enemy colony. If you have an inland expedition that will block off a competitor, but they have an expedition nearby that will finish sooner, it's often useful to contest their expedition so that your inland colony can finish without allowing them to contest it. Once you've blocked them off, withdraw and spend the points elsewhere.
One should not spend time colonizing provinces that cannot be reached by others if there are provinces left that can. There is plenty of time after the hectic period of the scramble to wipe up the last parts of Africa. Provinces that are unreachable by any other nation can wait.
Ideally you will see France, The Ottomans and UK fighting each other for the Libyan desert while you colonize all the way from Sokoto to Ethiopia.
Nations that have a favorable position to colonize Africa
This is a list of nations, that have a good position to colonize Africa. Most civilized nations can use this guide, but these are especially good relatively to their size and power.
- United Kingdom: There is seemingly not a single aspect where United Kingdom is not in a favorable position, but it is even more apparent when it comes to colonizing. The biggest navy in the game, good literacy and multiple colonies in both Southern and western Africa.
- France: They do not start out with a large navy (relatively to the size and power of France) but it has many coastal provinces and can easily build a big fleet. It does also have colonies in both eastern and western Africa.
Spain: The Spanish Armada is the second biggest navy in the game and a workable literacy rate. Unfortunately it has a lot of colonization points tied up in 
Philippines and their Caribbean Islands, but it should be possible to gather more. It has the island of Fernando Po from which it can reach Cameroon.- Denmark: A single province in Africa, a huge navy compared to Denmark's size and the best literacy rate in the game. Unlike the other nations Denmark might struggle to be a Secondary power by 1870.
- Portugal Large colonies in southern Africa and a big navy. Like Denmark it might however struggle to be a secondary power by 1870.
- Netherlands: A single port colony in Ghana allows a position to potentially colonize rich areas.
Attacking any of these nations, especially the biggest ones, in the 1860s and sinking their whole navy to the bottom of the sea will remove a major competitor and allow to easier grab a larger slice of the continent.
Last tips and tricks
These are small tips that do not really fit anywhere else.
- The Uncolonized part of Eritrea is one small province. It is advised to leave it open, so the others spend time on that while you colonize Somalia (which is much larger and more important).
- On 31 December 1869, pause the game and look at which nations are in the top 16 (and maybe the nations 17th and 18th to see if they are close to taking over 16th place). There is no need to block off Portugal if they are not able to colonize.
- Most of Africa has a life rating of 15, but Mozambique and Sena have a life rating of 35 which means that they can be colonized from 1836.
- If a great power borders Transvaal when gold is found in Witwatersrand, the event Witwatersrand Gold Rush will happen. This event gives a free conquest casus belli against Transvaal.