As always, start with Wikipedia:
http://en.wikipedia.org/wiki/Allied_intervention_in_the_Russian_Civil_War
The most significant by far was the Japanese force sent to Siberia, som 70,000 troops. Arriving in 1918 they were withdrawn in 1922.
The Allied forces, Whites, and various nationalist forces opposing the Reds were a hodge-podge, and no two of them were on the same page. While the Reds weren't military elites either by any stretch they at least were working toward a common goal and cooperated with one another for the most part. Their eventual victory was due to this more than anything else.