I don't know enough about this specific topic to give you more info than Wikipedia could, but:

• The Russian empire goes into WW1 controlling more or less the post-WW2 borders of the Soviet Union. It has Finland and eastern Poland as well, plus a few other diffferences, but you get the idea.
• Russia collapses in the war, several years of civil war ensue, the Bolsheviks win and name the new version of Russia "the Russian Soviet Federative Socialist Republic". It should be noted that the civil war was not at all just a "rebels vs government" deal, the list of different factions is utterly ludicrous. There was an enormous heap of different groups in the former empire and basically every European country was backing at least one of them.
• The RSFSR does not control all of the former Russian empire, only most of it. Several parts did their own thing during the civil war and are currently independent, often fighting their own ongoing civil wars. The RSFSR begins a bunch of wars to try to regain all of the former territory, losing some and winning others.
• The RSFSR regularly backs allied factions in the various national struggles, such as backing the Bolshevik-aligned Ukrainian Socialist Republic against the also-socialist but German-backed Ukrainian People's Republic, the anarchist Makhnovshchina movement, and the also-German-backed but not-socialist Ukrainian State.
• In the cases that the Bolshevik-allied factions won, you now have a bunch of Bolshevik-aligned states outside of the RSFSR.
• Delegates from the Russian, Ukrainian, Belarusian, and Transcaucasian soviet republics (Transcaucasia is today Armenia, Azerbaijan, and Georgia) get together at the end of 1922 for the First All-Union Congress of Soviets and agree to make a sort of country-of-countries. Something a bit like the EU, but communist and with more power centralised in the new government. This new thing is the Union of Soviet Socialist Republics. Nominally all four "union republics" are equal, although Russia remains enormously more powerful in practice than the others.
• One of the early principles of the Bolsheviks was equal rights for the various nationalities in the new state that they envisioned. To this end, they had a Commissar for Nationalities even before the revolution, a position whose job it was to make sure the nationalities got represented. This position was held by none other than Joseph Stalin.
• Over the next twentyish years, a number of regions in the four SSRs are broken off into new SSRs for different nationalities - Turkmen, Tajik, Uzbek, Kyrgyz, Kazakhs, and more out of Russia, Trancaucasia gets split into Armenia, Azerbaijan, and Georgia etc. Several conquered countries like the Baltic states also become union republics. I have no idea what logic was used when deciding which ones got to be their own republics and which just got to be autonomous parts of the RSFSR. A policy called korenizatsiya is implemented, under which people are meant to be able to run their lives in their own languages.
• The Kazakh and Kyrgyz SSRs stand out because they were autonomous regions of the RSFSR for quite a while before becoming their own SSRs. Their Central Asian neighbours in the Tajik, Turkmen, and Uzbek SSRs became union republics pretty quick, and others like the Bashkirs and Tatars stayed part of the RSFSR until the Soviet Union collapsed. It was only really those two that were somewhere in the middle.