Lenin led the Bolsheviks and Trotsky led the red army. When the Bolsheviks took power, they were a small unpopular government but Lenin in a very short time passed decrees, which satisfied the people and set up a strict secret police, which squashed opposition completely. Lenin used many methods to make his government strong but winning the people over certainly was a major factor as well as the fact that he was strong. Firstly, the power of the red army who were led by Trotsky meant that the Bolsheviks were well disciplined because there were harsh rules if any soldiers stepped out of line. Secondly the Bolsheviks got rid of their opposition. In November decrees Lenin allowed self-determination, which allowed people to act or decide for oneself. Also the Abolition of titles and class distinctions this meant that officer could no long be called by noble titles (His Excellency).
Also to win the civil war, Lenin introduced war communism, which was the economic policy, which existed in Soviet Russia during the civil war (1918-1921). The main features of war communism were that industrials were nationalized and strict centralized management was introduced. State control of foreign trade was introduced and discipline for workers was strict and striking was not allowed. Also when the war was over and his own supporters e.g. Kronstadt began to turn against him for his strict rules, he introduced NEP. This helped to make them strong because it helped stimulate the economy and it gave the Bolsheviks more supporters. The NEP helped to produce more agriculture, production of steel, electricity, pig iron etc. The NEP also allow free trade union, this increased the amount of trading done in Russia.
By signing the Treaty of Brest-Litovsk, Lenin could get Russia out of the war with Germany and then focus on the war inside Russia between Reds and Whites. By winning the civil war he got rid of his opposition, which were the whites, Tsarist supporters, Liberals and the provisional government. People supported Lenin. The workers liked the Bolsheviks because the Bolsheviks were mainly were on the side of the workers. They limited the working days to 8 hour and make decrees that helped the workers.
Lenin used propaganda like posters that said good thing about the government to show that the Bolsheviks were defenders of Mother Russia and of the success of the Revolution I think the most important reason they grew strong was because the Bolsheviks had great leader like Lenin who was a brilliant speaker and clever Politian who had good ideas and was unafraid to share his ideas with the public. Another good leader was Trotsky who was a brilliant but arrogant military leader who commanded and trained the red army, with his harsh rules and respect among the men; he had a well-disciplined army.