Communism was established by Lenin in one particular form, War Communism, from 1918-1921. However, he then replaced it with something rather different, the New Economic Policy, or NEP, which continued for a few years after his death in 1924.
Broadly speaking, communism refers to the political system in which industry, agriculture, banks, and all major societal institutions, are run by the state. This certainly happened for a time following the Communist Revolution in Russia in 1917, with the advent of War Communism. This was during the bitter civil war that sprang up in the wake of the Revolution.
Lenin struck a deal with the Germans that ensured Russia's withdrawal from World War I (the treaty of Brest-Litovsk), but he had an even bigger problem to deal with at home. His Bolshevik Party, which had accomplished the revolution - and was formally re-named the Communist Party in 1919 - still had many enemies in Russia who deplored the overthrow of the old order, and a bitter civil war broke out. War Communism was implemented more or less as an emergency measure during the exigencies of this war. Industries were nationalized, rationing introduced, private enterprise outlawed. Perhaps most strikingly, food was forcibly seized from the farms in order to sustain the army and people and workers in the towns and cities. This was a hugely unpopular measure among the peasants.
War Communism was not a carefully set out policy but rather one which Lenin quickly introduced in order to centralize all forces in his bid to defeat the enemy during the civil war. However, once the Communists had won, it became clear that, while War Communism had been readily enforced under war conditions, it hardly looked like a viable system now that the war was over. Economic productivity had slumped, and the peasants in particular had no interest in raising food when they couldn't keep any of it for themselves.
So, in 1921, Lenin introduced the New Economic Policy (NEP) which in many ways marked quite a significant retreat from Communism. For instance, nationalization of industry was partly withdrawn, although the biggest industries and banks remained in the hands of the state. A limited form of private enterprise was once again allowed. And food was no longer forcibly taken from the peasants who instead now had to pay a tax, which they found far more acceptable, as they could keep some food for themselves. The economy stabilized. After the turmoil of revolution and civil war, things finally seemed to be normalising - until Lenin's illness and death in 1924, which marked the beginning of a new power struggle at the head of the state. Stalin ultimately emerged victorious, and he ended the NEP in 1928 and went on to unleash a programme of centralization more brutal than any seen before.