How did the Mexican Revolution affect the United States? In what ways did American intervention in the Revolution lead to the United States’ entry into World War I?

The Mexican Revolution was mostly an internal Mexican matter and therefore did not have a huge effect on the United States. Its biggest effect was creating uncertainty in United States–Mexican relations considering the constant regime change in Mexico during the ten-year struggle.
At first, the United States generally followed the policy of supporting whichever Mexican regime was in power at any given time. This changed in 1913 when American diplomatic actions helped bring down the Madero regime. After Huerta took power in Mexico and murdered his political rivals, the United States severed diplomatic relations with its southern neighbor.
This all created a very unstable situation along the border. Things were exasperated when Mexican forces led by Francisco (Pancho) Villa began raiding border towns in New Mexico. President Wilson sent the US Army into Mexico in a failed attempt to capture Villa. Occasional raids along the border would continue throughout the conflict, which further damaged relations between the two countries.
As far as leading the United States into World War I, it would be incorrect to say that there was a direct connection. However, several incidences helped push the United States closer to entering the conflict. The first was the Ypiranga incident, in which the United States occupied the port of Veracruz to prevent the docking of a German merchant ship carrying arms for the Huerta regime. This highlighted Germany's willingness to help Mexico at the expense of the United States and showed America's resolve in preventing it.
Mexico was the center of another episode which brought the United States and Germany even closer to war. This was the Zimmerman Telegram, in which Germany offered to support Mexico if they invaded parts of the southwestern United States. While Mexico never seriously considered Germany's offer (they were too busy with their internal revolution), this telegram heightened anti-German sentiment in the United States.
https://education.texashistory.unt.edu/lessons/psa/failed_diplomacy/

https://www.loc.gov/exhibits/mexican-revolution-and-the-united-states/timeline.html