Where have you seen it suggested it was easy?

Anyway, it wasn't, really. I'm not exactly an expert, but summarizing some points:

The British were very good at making the local rulers fight each other. This alleviated the need for British fighting (for which they used locals, sepoys, but still) and allowed them to divide and conquer, as the saying goes.

India had a long history of bribes being used in warfare. I don't remember where I read about this anecdote, but apparently there was a fortress that changed hands four times in one war, by the defenders (at that point) being bribed. The British had a lot of money and gladly used it.

This point will also speak to your question about technological superiority. In short, the Indians were not technologically behind by very much. Locals very effectively managed to adopt European weaponry and tactics, though they needed European advisors (often Brits). One amusing example is that the British government imposed a tariff on ships because the Indian shipbuilders became better at building European style wooden ships than British shipwrights. Anyway, as you might expect, the British and other European officers weren't particularly loyal to local rulers, so it often happened that they were bribed by the Brits.

This isn't to say it was easy; the British lost a few wars too. I couldn't tell you how many, though, you would have to consult the literature or an actual expert. Below is a list of literature I've read. It focuses mostly on technology and warfare.

Articles

G.J. Bryant, "Asymmetric Warfare: the British Experience in Eighteenth Century India", in: The Journal of Military History 68 2 (2004) 431-469.

A few articles by Jos Gommans might be useful, but I realized that you might not have access to them anyway. If you do, you can just look for them on worldcat, otherwise, oh well. The title above is very useful though, so I'll keep it here.

Books or chapters in books

Gommans, Jos, "Warhorse and Gunpowder in India c. 1000-1800", in: Jeremy Black (ed.), War in the Early Modern World 72-85. This chapter includes a very detailed and extensive bibliography divided per subject.

Idem, Mughal Warfare. I don't have the other bibliographical details on hand at the moment.

...was it because of the huge amount of small, petty kingdoms without any unity that additionally made this so easy for the British?

The absence of a large national consciousness did make it much easier to play various groups and people with different political ambitions off against each other in ways that would improve the East India Company's situation. Their growth of power in South Asia initially started more as economic and political opportunism to strengthen their trading position and to extricate their French enemies from their would-be sphere of influence. I don't think there was a concrete plan in the early days of the East India Company to effectively rule South Asia, but there were always officials on the lookout for political situations they could use to their advantage. The land management system the Mughal Empire had set up certainly helped as well, so I'll talk about that too.

Here's some of what I wrote a couple days ago related to all this:

The British had a lot of economic incentives to focus on India... These became quite strongly tied to political incentives in the mid 18th century during conflicts between the French and British, i.e. the War of Austrian Succession and the Seven Years War. These initially bled over from Europe into South India where the British and French East India Companies both had trading bases, the British in Madras (now called Chennai) and the French in Pondicherry. (Here's a map so you can see the relative positions of the cities- they're not extremely far away.)

Now in the 18th century, the British East India Company was still privately owned, unlike the French one that was largely controlled by their government, though the British government was still willing to invest troops in protecting their trading interests. The French Governor-General of India at the time was also interested in using his Company's power to expand French influence and territory in India, a wish threatened by the presence and strength of the British (and one which the British eventually felt threatened by.) This turned into a situation where the French and the British were willing to fight to extricate the influence of the other from South Asia, and kicked off what are called the Carnatic Wars. They eventually involved both powers involving themselves in local politics and exploiting political situations to strengthen their own positions and influence, and ended with the French being effectively neutralized as a power not just in South India, but in South Asia as a whole. This left British interests in a very strong position, and directly lead to them essentially becoming a political power with tax-collecting authority over Bengal and surrounding areas.

Despite my talk of South India, the East India Company gained its first major center of power in Bengal. The Mughal Empire's revenue collection system actually fed into the result of British desire to better their economic position and be rid of French enemies/competition in such a way that it enabled them to gain a strong foothold in South Asia politics in the first place. It also helped create the various interests that could be played off against each other, as I said and which you alluded to. Anyway, a stretch of land, a jagir, would be awarded to a highly ranked member of the aristocracy in the Mughal Empire. Jagir assignments would often be transferred; it was not intended to be a permanent assignment. Revenue from the jagir based on what it produced would be collected by a zamindar- these were local rulers/officials who would keep a portion of the sum for themselves. As time went on, there was less and less new land to incorporate into the jagir system, so advancing bureaucrats could end up with very small assignments or none at all. Powerful zamindars afraid of losing their land rebelled against central Mughal authority, and ended up becoming nawabs (like governors) of autonomous or semi-autonomous regions, like Bengal and Awadh. This started in the late 17th century and the positions eventually became hereditary, so if you were the Nawab of Awadh, the Mughal Emperor couldn't just pass off Awadh to some other aristocrat. One consequence of some of what I said was that the East India Company could initially pick and choose which zamindars they would do trade under, support, and buy land from.

Okay, so the Nawab of Bengal in the 1750s, Siraj-ud-Daulah, really didn't like the British and was unhappy with them for three reasons. He was upset that they were exercising privileges not outlined in agreement with the Mughal Empire (their firman), that they were harboring political dissidents in Calcutta, and that they refused to demolish the Maratha Ditch. (The ditch was a structure that the British dug around the city to defend it against Maratha raids, though the Marathas had been pacified by the Nawab ~6 years prior so the ditch was no longer necessary. It was also paid for by the local people, not by the Company, and built without permission, so the Nawab felt the British were overstepping their authority.) Siraj-ud-daulah attacked the East India Company's fort in Calcutta and captured it. The British retaliated and took it back, also taking the French trading center in Chandernagore to crush their trade competition, as I already talked about.

The Nawab withdrew and began correspondence with the French regarding a possible alliance, but before anything could be done he was betrayed by his commander, Mir Jafar, who had gone over to the British side in exchange for being made nawab once Siraj-ud-daulah was defeated. This was the 1757 Battle of Plassey. After the battle, Mir Jafar was made nawab, only to be replaced when he denied the East India Company more land and revenue rights. Mir Qasim, Mir Jafar's son-in-law, took his place, however he too was not as lax as the British hoped he would be, as he had an issue with the Company doing more than their firman said he could. He was overthrown, and Mir Jafar was re-installed. This is a prime example showing how the East India Company was able to successfully navigate the political climate in South Asia and use it to their advantage, becoming powerful and influential enough that they were able to install puppet rulers and change them up at will.

The deposed Mir Qasim went on to ally himself with the Nawab of neighboring Awadh and the then-Mughal Emperor Shah Allam II to fight the British about seven years later; they lost. The East India Company was able to force the Emperor to give them the diwan of Bengal, legally enshrining the East India Company as the most superior revenue collecting body there, and forcing Awadh to ally with British Bengal, becoming both a puppet and buffer state.

Something similar later happened in southern India, where the East India Company was able to re-install a previously-ruling family (the Wodeyars, who are actually still around today) to the throne of the Kingdom of Mysore, which from then on existed under Company watch until it was incorporated as a semi-autonomous princely state within the empire.