Aha! Finally a question that falls into my area of knowledge
Sino-Soviet relations quickly deteriorated in the 6th decade of the 20th Century, namely after the 22nd Congress of the Communist Party of the Soviet Union was held in October 1961 - this was the last Congress Chinese representatives attended for quite some time, and financial/military aid from the Soviet Union to China gradually came to a halt. Soviet experts within China were also recalled - a huge blow to the young nation's industrial and R&D efforts.
To my knowledge, there are many reasons for the falling-out. Here are a couple:
-First off, keep in mind that it's very difficult for two major countries to maintain good diplomatic relations, especially considering the historical struggles between the two, the border disputes, and last but not least national security and interests at stake. If there are those not very familiar with this segment of history, think Germany-France relations... There are many more individual events that contributed to the cause, however they're numerous, and unfortunately, I don't know too much about the details of every specific event, but I will try to give a quick, and hopefully insightful rundown about the ones I do know about.
-Ideological: The Soviets tried to avoid large-scale conflicts and nuclear showdowns with the west as much as they could, believing that the revolution would be rendered meaningless if everyone was dead, and the world was destroyed. On the contrary, it was an open secret within the Chinese Communist Party that Mao wished to bring about a third world war, in which imperialism would be eradicated, and after the exchange of nukes, a few million western survivors would be overwhelmed by hundreds of millions of Chinese. Also, the Soviets weren't exactly on board with the idea of the "Great Leap Forward", and the People's Commune, believing that they don't adhere to the true communist ideology.
Historical struggles: There have been border disputes between the two countries for thousands of years, and neither Stalin nor Khrushchev were too eager to stick to Lenin's promise that all territory seized by the Czars would be given back to the Chinese. The Soviets encouraged outer Mongolia to separate from China, and even to this day, they still hold Vladivostok and over 1.6 million km2 of territory ceded to them by the Qing dynasty after various unequal treaties, so there's that.
National Interests - During the closing stages of WW2, the Soviets invaded Manchuria, and absolutely destroyed the KuanTung army within weeks. However, when they left after the surrender of Japan, they virtually took everything of any value - namely factory machinery and all the riches that the Japanese have accumulated through various means - namely via systematically killing Chinese civilians and taking their savings. Also, during the Chinese Civil War, even though the Soviet Union supplied the Communists with weapons, their support wasn't as much as Mao had initially hoped for, which made him very unhappy. (the Soviets also signed a treaty with the Nationalists in 1945)
Misc. Events: Essentially, Mao and Khrushchev held a meeting before the Second Taiwan Strait Crisis took place, and Mao had claimed that they were talking about matters concerning national security, thus naturally after hostilities commenced US and co assumed that China had the backing of Ivan. That was not the case... They didn't talk about anything important at all, and Khrushchev felt exploited. What's more, the Chinese initially refused to hand over an AIM-9 Sidewinder missile they captured, and understandably, the Soviets weren't too pleased about that. The Soviets also wanted to cooperate with China on the development of a long-wave radio system, but Mao ignored them, claiming that it was a matter of state security, and it threatened key national interests.
The Zhenbao Island conflicts (a border dispute in which the Soviets were the aggressors, hundreds of soldiers were killed on both sides, China acquired a T-62 tank that was abandoned, and a Soviet colonel was killed by artillery fire) and the incidents in Prague worried the Politburo, and the Chinese started calling for "defeat of Soviet Revisionism" (for the lack of a better translation - 打到苏联修正主义）
(These are just a couple off of the top of my mind, please excuse me if I'm missing some key points here)
During Vietnam's struggles to gain independence from the French, the Chinese sent supplies, weapons, food, and even military advisers to help them modernize their military and drive away the 'imperialists'. This was a time when China was still rebuilding, and Mao had his own citizens starve in order to support the revolutionary movements in Vietnam, which is somewhat ironic and sad considering what happened next.
Similar to what North Korea are doing right now; after the French were driven out and Vietnam declared its independence, they were quick to claim that it was them that did all the work, that outside aid was but a very small factor in their success. That, compounded upon by border disputes and the prosecution and discrimination of Chinese people in Vietnam, led to the Sino-Vietnamese war. After the "Ping Pong Diplomacy" broke the ice between the US and China, relations between the Soviet Union and China further worsened.
The Soviets supported the Vietnamese, who also used an odd lot