Christianity coalesced into a unified church in the early fourth century, centered upon the Council of Nicaea, sponsored by the Roman Emperor Constantine in 325. The first major split occurred because of differences in the eleventh century. The Western church had the Pope as basically the supreme power in Western Europe because of the fall of the Roman Empire. However, the Easter part of the empire did not fall to invasions and reformed into the Byzantine Empire, which lasted in some form until 1453. as such the patriarch (basically an eastern Pope) was completely subservient to the Byzantean emperor. When Pope Leo III crowned Charlemagne Imperator Romanum, "Emperor of the Romans", in 800, the Byzantine Empress, who saw herself as the most legitimate heir to Rome, took offense. These problems were exacerbated by a number of doctrinal conflicts, particularly whether or not it was permissible to create and sell Icons (holy images). the great split finally occurred in 1054 when the Pope and the Patriarch excommunicated (banished from the church) each other. Those in the West who followed the Pope became known as Catholics, and those who followed the Byzantean Emperor and Patriarch became know as "Eastern Orthodox Christians". This is the story of one branch of Christianity. If you want to hear about the others I'd be happy to, but it will take a while.

You are asking about the history of hundreds, possibly thousands, of groups. I would suggest narrowing the scope of your question.

Also you run into the problem that 'denomination' is a relatively recent construct of an idea, and there are questions about what a denomination 'is', both historically and theologically, as well as what counts as a 'Christian' denomination and what counts as a distinct religious grouping.

There is continued debate over early Christianities and how unity and diversity worked in them. My own view is that while there was plenty of diversity, communities exhibited a strong sense of unity that was underwritten by commonalities that developed into a mainstream church which considered itself Orthodox over against smaller fringe groups. The first point at which you get something resembling an alternate church structure that one might call a denomination would be Marcionite churches from the mid to late 2nd century onwards.

On this reading, I think /u/Arathnorn does a bit of disservice by suggesting a 'unified church' didn't come into existence until 325. The church within the Roman Empire was plenty unified before Constantine came along, and the problems that lead to the major split in the 11th century emerged long before then.

But one shouldn't skip forward to the 11th century anyway. In the 5th century you see the emergence of the first real, significant 'split' in the church. By this time Syrian-speaking Christians in the Sassanid Empire are a significant group with loose ties to Roman Christianity, and the debates around Nestorius in the 5th century lead the bulk of the Syrian church to reject the Council of Chalcedon in 451 and thus you get the major 'denomination' of the Church of the East (also, but unhelpfully and inaccurately, known as the Nestorian church). The same event acts as a catalyst for another group of non-Chalcedonian adherents to form the Oriental Orthodox communion, which likewise exists mostly outside the reaches of Rome, except for its strong influence in Egypt. So you have a three way split halfway through the first millenium, which a lot of people are ignorant about.

The Roman Catholic/Orthodox split formally occurs in 1054, but it's the result of a process of cultural, theological, and political divergence over several hundred years, and in many ways the two churches were functioning independently well before 1054 made it 'official'.

However, the proliferation of denominations today are mostly variants of Protestantism, which have their roots in the Reformation in the 16th century. I will leave that for someone more well-versed in Reformation history to cover, but perhaps I will chime back in later.