Well, gosh, this type of question will require a whole book to answer fully, but I'll give it my best.

The place to start is nineteenth-century linguistics and one of the words that Russian has given to the world: intelligentsia. As the Russian state modernized, there was a class of educated individuals, singularly called intelligent, who were alienated from the autocratic Russian state. The question for many of these intelligent was, to borrow the title of one Lenin's works, "what is to be done?" Some of these intellectuals gravitated towards the liberalism and a form of Russian nationalism. Often called the Kadets (constitutional democrats), these became the establishment opposition in the tsarist state. For other intellectuals, the solution was to be found in the Russian peasantry and its traditional communal living. These groups, loosely called populists exerted a strong influence amongst intellectuals of a romanticist inclination. Other intellegent drifted towards Marxist socialism, but were torn by how to achieve a revolution in Russia. One faction, termed Mensheviks, believed that a proletarian revolution could only come with the development of capitalism within Russia. The other faction, famously known as Bolsheviks, contended that a vanguard of die-hard activists, called a vanguard, could act at a strategic moment and push Russia towards a revolution that would become a proletarian one. The division between Menshevik/Bolshevik was often a hazy one and many individuals drifted between the two groups. And of course there were other individuals who were anarchists, and floated between these underground groups.

The Russian state acted to this mushrooming of opposition with its characteristic lack of subtlety and treated any call for reform as hostile to the Romanovs. The 1905 Revolution gave a hint of how bad this strategy was when defeat in the Russo-Japanese War uncovered a lot of the tensions within the empire. The Russians deployed troops to forcibly disperse the protesters, many of whom were initially calls for peaceful reform. Tsar Nicholas II eventually relented and granted a limited constitution, but the damage to imperial prestige was done and the 1906 constitution was a deeply flawed document that satisfied few political groups. The populists formed political parties, often termed Socialist-Revolutionaries (SR), but boycotted Duma elections. Many of the underground activists predicted that the next crisis would be a perfect opportunity to destroy the imperial edifice. The protracted defeat of the First World War provided just such an opportunity.

Although standard convention is to refer to 1917 as the Russian Revolution, there were actually two separate revolutions. The February Revolution was prompted by street protests in Petrograd and the state's failed attempt to use force to subdue them. This first revolution directly led to the creation of the Provisional Government under the leadership of the Kadets and the abdication of the tsar. The new Russian state was to be a democracy, but the Kadets also committed themselves to continuing the war against the Central Powers. This was an enormously unpopular decision among the radicalized urban workers, who formed groups called Soviets, and the Provisional Government's increasingly anti-democratic tone gave activists an issue to rally around. This was where the Bolsheviks came in and they took advantage of the situation and their importance in Russian politics grew. The Provisional Government replicated the mistakes of their predecessor and tried to shut down the Bolsheviks through force. This seemingly authoritarian turn made the Bolsheviks the de facto champions of the revolution, even though most Soviets were affiliated with the SRs. The Bolsheviks capitalized on their opportunity and seized power in the October Revolution under the slogan "all power to the Soviets."

The Provisional Government evaporated under this pressure, but the Bolsheviks found that exercising power was quite a difficult task. There were strong nationalist and anti-Marxist forces, called Whites, who fought against the revolution and used the Bolshevik's seizure of power as a pretext for violent counter-revolution. The Bolsheviks gradually began to act more dictatorially under the pressures of simultaneously fighting the civil war and trying to control the revolution. Most of Russia's peasantry preferred the SRs and in the 1917 election to the All Russian Constituent Assembly, the SRs won 40% of the vote to the Bolsheviks 25%. The Bolsheviks in Moscow decided to ignore the results of the election and dismiss the Assembly. The Bolsheviks eventually triumphed over the Whites, who were a rather motley group with divided goals, but the process was highly bloody and there were atrocities on both sides. Many Bolshevik leaders began to govern by fiat and under the maxim the ends justifies the means, and this led many reformist individuals to become disappointed with the outcome of the 1917 because revolutionary fervor and a sincere desire to transform the world had been replaced by careerist apparatchiks who gave lip service to social transformation.

If you want to learn more, one of the best introductory textbooks is Ted Weeks's Across the Revolutionary Divide.