Install a new system of government
Bolsheviks aimes to install a 'dictorship of the Proletariat' as soon as they got into power. They wanted to install a government which would rule in the interests of the working man until he could rule for himself.
Establish Russia as a Soviet Socialist Republic
This was another of the main objectives. This was declared in the Constitution of 1918.
In 1922, Russia was then declared a Union of Soviet Socialist Republics with 5 other countries.
End the distastrous war against Germany
This was promised in Lenin's April Theses. After the mass desertations of soldiers in summer of 1917 and the invasion of Germany into Russia, the Bolsheviks were forced to sign the Treaty Of Brest-Litovsk in March 1918, effectively ending their war involvement.
Become a one-party state
To do this the Bolsheviks needed to eliminate opposition. They received opposition from a variety of groups inclusion Mensheviks and Tsarists. In the elections for the constituent assembly, the Bolsheviks were far from most popular with Socialist Revolutionaries dominating the vote in the countryside: 370 votes to 175. The Constituent Assembly was dissolved and this potential opposition removed.
Provide themselves with means to control the count
Bolsheviks still needed to spread their power across Russia. Therefore, a party bureaucracy was established by 1921, giving them control of the police and army. This was consolidated by 1922 when the Central Committee for the Communist Party was established. Many believed the revolution in Russia was only safe if they had Communist neighbors and so Lenin hoped the Red civil war victory would encourage world revolution.