Hey, sorry it took a few days to get to this question.
CptBuck is correct that Islam first enters Africa during Amr ibn al-As' campaign in the early 640s AD. For a blow-by-blow account of the spread of Islam across the Mediterranean shore, i'll refer you to an earlier post I wrote.
After Islam spread to the Atlantic, it then made the hop across the Sahara in the mid-8th or early 9th century, conveyed by traders. More about that here
Interestingly, while Islam was spreading westward from Egypt, and across the Sahara, for a very long time it did not make its way south up the Nile. This is attributable to the Bakt between Egypt and Christian Nubia, although this changed after the rise of the Mamluk sultans in Egypt, who began the conquest of Makuria and Alwa in the mid 13th century.
Only slightly after the conquest of Egypt, there was a raid on the Aksumite port of Adulis, and the establishment of a Muslim colony on the Dahlak archipelago in 702 AD, and subsequent conversion of Muslims along the red sea shoreline where is now Eritrea. However, Islam did not penetrate into the Christian Ethiopian highlands, until much later, when there was a conflict in the early 1500s between the Sultanate of Agaw (centered around Djibouti) and the Empire of Ethiopia where both the Portuguese and the Ottoman Empire intervened
Additionally, from the 7th century onward, traders from Arabia and Persia (later India too) established settlements on the islands off of the coast of East Africa. They quickly married local peoples, and formed the Swahili culture. Swahili trade developed trade linkages with other regions along the Indian Ocean basin until the early 16th century, when the Portuguese arrived and conquered many of the city states. However, the sultans of Oman were able to drive the Portuguese out.
A bit later, with the European push for exploration and access to markets in the interior, Swahili merchants would directly compete against this and begin to spread islam into the interior of East Africa in the later half of the 19th century.
Sorry for being lazy and only linking to old posts. Although I mention it several times in those comments, you really should read Levtzion and Pouwells History of Islam in Africa, because it is a fantastic book. Loumeier's Muslim Societies in Africa; a historical anthology and David Robinson's Muslim Societies in Africa are also decent overviews for the contours of the spread of Islam on the continent.
Aside from merchants who would have been going back and forth across the Red Sea, Islam first entered Africa with the conquest of Egypt by Amr ibn al-As in the mid 7th century and spread west until all of North Africa was under Islamic rule within the next 50 years.
As for how it changed Africa that's probably too broad a question to answer as it covers 1300 years of history. Some of the bigger changes would have been: the almost total supplanting of Christianity with Islam in the subject countries (the largest extant Christian population in North Africa is Egypt's Coptic Christians who make up ~10% of the population.) Likewise Arabic became the normative language, and although what it means to be an Arab is an interesting question the Islamic countries of Africa generally view themselves as being Arab as well despite obvious differences in things like skin color. Most of the largest cities in North Africa were founded by Muslims e.g. Cairo, and Algiers. It also created a huge exchange of goods and ideas between east and west, with the result that you end up with things like Persian qanats spreading as far was as Morocco.
edit: I'll add that I'm far less familiar with Islam in sub-Saharan Africa, and I'm afraid I can't be of much help there.