Well, from the little I know, many european countries sent forces in Russia, in order to help the white russians against the communists (Bolchevik and also Menchevik) until late 1919 : Germany, France, UK, etc. I think the US were also fighting against the Bolcheviks. Around 1920, Menchevik communists and anarchists were fired from the governement and turned against the Bolcheviks (mainly acting as terrorists).
The war against Poland ended in 1920 (I think the Bolchevik lost)
The Allies considered that Russia betrayed them by signing the Brest Litovsk treaty, and decided to cut the country into zones of influence (?) : the English near the white sea, the French got the black sea, Poland and Crimea, the Japanese got Siberia. But in 1919, most of them left the area, IMO because they had enough problem at home and not enough resources nor manpower to fight a foreign and endless war.
Once the Allies left, Trostky achieved to overrun the White Russians by turning the Red Army into a well organised, disciplined, 5.5 million men strong army (the fact many white generals were fighting among themselve kinda helped him btw).
Communist revolutions erupted in many countries : Germany of course (with the Spartakists) but also Hungary, in the 'Republic of Bavaria', etc. There were trouble in Italy an France aswell.

That's probably not the best source, but a french comic (Corto Maltese en Sibérie) shows IMO an accurate description of post WWI Russia.