How were the Bolsheviks able to seize power?
The original question had to be edited down. The Bolsheviks were able to seize power because the Provisional Government failed to effectively respond to the pulse of the Russian body politic. The Provisional Government and its practical leader, Alexander Kerensky, failed to effectively understand the condition of a vast number of Russian citizens. The Provisional Government could not give immediate answers to the peasantry's demand of land acquisition and refused to withdraw the Russian participation in World War I. Both of these ended up doing much damage and harm to the Provisional Government.
Contrast this position of perceived weakness to the Bolshevik position. The Bolsheviks were open about the redistribution of land and unconditionally withdrawing from World War I. In being able to bring out these two popular messages, Lenin and the Bolsheviks were able to tap into public discontent and galvanize this into action. Kerensky, encumbered by a nuanced and complex political position, could not counter this amount of zeal and support in something perceived as so elemental. It is here where the Bolsheviks were able to gain power, wrestling it away from the Provisional Government.