How can you find a list of men who served in the 311TH infantry in World War 1?

You would probably have to visit the National Archives in person and assemble such a roster yourself. Some WWI divisions published a divisional history after the war. I do not know if the 78th Infantry division was one of these. (The 311th Infantry was one of the four infantry regiments in the 78th Infantry Division in WWI). Some regiments also published a regimental history, and again, I do not know if the 311th was among these. Even if either a regimental or divisional history exists, these typically do not include a list of all men who served. A WWI US division had over 26,000 men at full strength, and regiments had over 6,000. When you consider replacements for those lost to sickness, accidents, wounds and death such a roster would include many thousands of men. Histories usually include a "Roll of Honor" of those killed, and often those who earned Medals. You could look on eBay and watch to see if a WWI history of either the 78th Division or the 311th Infantry is offered, but, again, I do not suppose that such a book would include a complete roster.

You might try contacting the divisional "alomni accosiation" to see of they can help:

http://www.78thdivision.org