The first temporary monument to the socialist icon appeared slightly on the different place than the today's one on Revolution Square on 7th November 1918 to commemorate the first anniversary of October Revolution.
Capital was just recently on 12th March moved to Moscow, square renamed from the Resurrection one, and the monument was to be an inspiration for all the soviet people under the widely propagated by Lenin "Program of monumental propaganda". Under the key objectives of that program any glorification of the Tzarist regime should have been removed and the grandeur of the newly established Soviet system emphasized.
Monument showed Marx and Engels and was personally opened by Lenin in front of key party members. Though because of its whimsy design it was instantly nicknamed "Two in a bathtub".
Marx was one of many opened in the city on that day and the years followed. But because of the material scarcity or sometimes the view of replacing them with something else later, they were mostly built out of very unreliable materials (like plaster of Paris) and not many survived. This one dilapidated and was removed less than two years later
Almost right after that on 1st May, 1920 a little closer to the main road down the square, on the place facing the Bol'shoi, the first brick for the new monument to Marx was put. Draft was personally approved by Lenin. However, project appeared to be a typical Russian "dolgostroy" (long in the construction). Yeah, the phenomenon was so much not unique, that there's even a special word for it in the vocabulary.
Construction lingered for long after Lenin's death and till 1957 there was only one granite brick with inscription: "First stone of the monument to the great chieftain and teacher of the word proletariat (workers) Karl Marx". Then Kruschev's administration opened a competition for a new monument and a prominent soviet sculptor Lev Kerbel and his team were assigned to its realization. It was announced as a great event in all the media as the cutting was to be performed live by the architect himself from the enormous monolithic granite lump in front of the astonished public. Work lasted for several months and the finished project was finally solemnly opened on the 29th October 1961. Opening was attended by the highest party administration and even delegates from some foreign communist parties from around the world.
Finalized version weights 160 tons. Marx represented as an orator on a tribune addressing workers with a fiery speech. Although to some unprepared eye he may look a little like Santa Claus, preparing communism as gift for the naughty kids for Christmas;) Known fact that is was addressed by a prominent actress and critic of her days Faina Ranevskaya as a "Refrigerator with a beard".
Under Marx there's an inscription in Russian: "Proletarians (workers) of all counties unite!" And on two pylons on left and right from it two quotes respectively: "His name and his deeds will outlive centuries" F. Engels (said that on Marx's funerals) and "The teaching of Marx is all-powerful, because it is right" V. Lenin (just said that:).