The Bolshevik Revolution deeply concerned both Britain and the United States, and both nations sent troops to Russia during the Revolution and Civil War. American troops numbers were small and they played virtually no role in events, but Britain's involvement was larger.

The Bolshevik revolution was a shock to the Allies. They had no real idea of who the Bolsheviks were, nor an understanding of their plans and ideals. What mattered to them was that the Bolsheviks remained in the First World War, as the Provisional Government that followed the February Revolution and the abdication of the Tsar had done. However, the Bolsheviks soon made it clear that they had no intention of honoring their alliance, and this is where the trouble came from.

Britain worried that if the Bolsheviks made peace with the Central Powers, thousands of enemy soldiers could be transferred from the Eastern Front to France. Moreover, the Central Powers could limit the effects of the British blockade of Germany by seizing agricultural land in Russia. They could also potentially liberate thousands of prisoners of war held in Russia, and capture the tons of war material that the Allies had sent to Russia over the course of the war, most of which was still sitting in the ports where it had been offloaded. The Allies were confronting a strategic nightmare if Russia dropped out of the war.

The Bolsheviks made things worse by reneging on Russia's huge debts to Britain and France, and then publishing secret treaties made between the Allies that embarrassed them on the international stage. In March 1917 they did indeed make peace with the Central Powers with the Treaty of Brest-Litovsk, leaving Germany in control of a huge swath of Eastern Europe.

The Allies decided to send troops to Russia to reconstitute the Eastern Front and keep the Germans occupied. They hoped that America and Japan would be willing to send large expeditionary forces, but Wilson was unwilling, and while the Japanese did send some 70,000 troops to Russia, they were more concerned with stealing Russian resources than fighting the Germans, and never left the Russian Pacific shore.

This forced Britain to turn to proxies. First was the Czech Legion, a Russian military unit of Czech and Slovak prisoners of war. The legionnaires had gotten on poorly with the Bolsheviks, and in the spring of 1918 had started an open war to break out of Russia and go back home. The Allies convinced them to stay in Russia and fight the Germans instead.

This is where things get a little confusing. No one really knew who the Bolsheviks were or what they wanted, and most British military officers figured they were probably German agents (which was partially true, although the Bolsheviks had their own goals and were not working for Germany). So while Britain wanted to fight the Germans in Russia, it had no real qualms about getting involved in a burgeoning civil war between the Bolshevik Reds and the anti-Bolshevik Whites.

The Whites were the other groups that Britain turned to to fight in Russia. The Whites were a mixed-bag of counterrevolutionaries, loosely aligned and spread across the former Russian empire. They pledged to retain their commitment to the Entente and help fight the Germans, so Britain sent them cash, equipment, and advisors to help. This was Britain's biggest role in the Russian revolution, as a supporter of the White forces.

Britain and America also sent some fighting forces to help the Whites, but whereas the plan had been to fight Germans, the onset of civil war soon meant the Allied forces were shooting it out with Russian Bolsheviks instead of Germans. The biggest Allied troop deployment was in Archangel, where several thousand British, American, Canadian, and French troops landed to form the nucleus of a White Russian army. They got involved in fairly miserable trench fighting with the Bolsheviks in the winter and spring of 1918-1919 before being evacuated. Elsewhere the Allies did not contribute much in the way of fighting troops, but Britain's role as a supplier of arms sustained the White war effort throughout 1919. When it became clear that the Bolsheviks were going to win the war by the end of that war, the Allies disengaged with the Whites. The policy to support them had never been widely supported anyway in Britain anyway and had more to do the support of junior British military officers in Russia than high-level decisions in the Britsih government.

Tl;dr - Britain and America sent small numbers of troops, and Britain sent a lot in the way of cash and weapons to the White armies in the Russian Civil War, but they wanted to fight Germans, not reverse the Russian Revolution, at least at first. In the end their support was not enough to turn the tide of the Civil War.

I'm sorry, this answer is a bit jumbled, but that is a huge question, and the Allied intervention in the Russian Civil War is widely misunderstood on both sides of the former Iron Curtain. Please feel free to ask more specific follow-ups and I will gladly try and explain more! This is a fascinating topic but one that is deeply complicated, and I even have some unorthodox opinions about it that I rarely get the chance to share.