Stalin: Rise to power

Lenin's funeral

Stalin told Trotsky that Trotsky would not have enough time to arrive for the funeral. Therefore, Trotsky did not attend and it looked as though he could not be bothered to turn up. Stalin made a speech about the mantle of Leninism in order to transfer the cult-like image of Lenin to Stalin. Lenin did not want a luxurious funeral, but Stalin gave one and the people saw Stalin as a 'disciple' of Lenin instead of Trotsky.

There were also issues in which the government could not have a consensus on.
Permanent revolution vs. Socialism in one country
For Trotsky, he believed that the Communist revolution would not succeed in Russia because Russia's working class was too small and the economy was underdeveloped. Russian would continue fighting until world Communist revolution was achieved, thus putting Russia in a state of permanent revolution.

For Stalin, he appealed to nationalism and patriotism, allowing for Russia to take the role of a unique position and show the world what socialism meant.

NEP and industrialization debate

The NEP already appeared unattractive as it saw growth of rich class, property dealing, land speculation, gambling and prostitution. The government was also internally split on how to deal with the NEP.

The left wing (Trotsky) wanted to end NEP and go for rapid industrialization which meant that labor would be militarized, peasants' power on the economy would be broken, and peasants' grain would be squeezed out of them to be used for industrialization.

The right wing (Bukharin) wanted to keep NEP going and encouraged peasants to become richer by spending more consumer goods to lead to growth of manufacturing industry.

Stalin's positions
Stalin already worked in key party organizations such as the Politburo, Orgburo, Secretariat, and General Secretary.
As party secretary, Stalin had control over what was discussed and what information other members received in Politburo.
Being in the Orgburo and as the Secretariat allowed control of appointments to positions of responsibility in the party structure. Therefore, Stalin could put his supporters in key positions and party secretaries from regional to local were Stalin's men.
Because Stalin controlled party organization, he could influence selection of delegates who were sent to annual party congress where major issues of policy were decided.
He also had control of party membership, allowing him to weed out radical students and soldiers.

Political maneuvering 
Lenin's secret testament consisted of criticism towards Zinoviev, Kamenev and Stalin. For this testament to be read out in public would destroy the reputations of the three. Zinoviev and Kamenev sought Stalin's help in defeating Trotsky and they thought Stalin was not a threat. Zinoviev and Kamenev began to attack Trotsky while Trotsky attacked back. Stalin, though, was in the background, watching the fight, which added to his reputation of a moderate peacemaker.

Stalin's idea of socialism in one country was popular and it attracted the right wing because it seemed to fit in with NEP as their own route to socialism. Stalin formed alliance with Bukharin, supporting the NEP and cooperation with peasants.
In 1925, Zinoviev and Kamenev attacked Stalin, but Stalin, having control of the delegates, outvoted those two.
In 1926, the two joined Trotsky to form 'United Opposition,' but was accused of factionalism and all three lost positions of power and expelled from party.

Stalin turned against NEP and attacked right wing. Stalin advocated for rapid industrialization and use of force to make peasants cooperate. Bukharin defended NEP but Stalin's delegates once again outvoted Bukharin and he was removed from party.

Other factors
Trotsky had too many weaknesses, such as being high minded, arrogant, and dismissive of colleagues, which probably led to his downfall. Trotsky also joined the party in August 1917, and therefore, was not seen as loyal. As well, he did not build a foundational power base like Stalin did and Stalin destroyed the one Trotsky had which was eroding.
Stalin's advocating for rapid industrialization had the majority support. He was seen as a loyal part member due to his proletariat roots. Stalin adopted policies that were approved by majority of Communist party. He was also lucky that Lenin's testament was not read out loud.