how do i find out the service record of a former US soldier.

[Mk VII]

If a former serviceman served in U.K. armed forces after 1939 you currently need to approach the MOD to access their service records but I don't believe that they have to give anyone access to the records. This may change in time if the records are released to public records. On a number of occasions, I have tried to find the service records of former British servicemen who served in both WW1 and WW2 but have never been successful. I concluded that the WW1 records were most likely held with the WW2 records by the MOD but I have not pursued the matter by contacting the MOD to ask. I, of course, don't know this for sure but it has been true in all the case which I have looked at.

Service records of personnel discharged before 1921 are available to public scrutiny at the National Archives in Kew (microfilms). People who re-enlisted later, as many did, are still held back.
The records office for WW1 ORs (or EMs if you're American) was bombed in 1940 and between a half and two-thirds of all records were entirely destroyed. Many of the remaining documents are damaged by fire and water. Records of officers, and of the Household Division, were stored elsewhere and are not affected.
Some records were removed before this to the Ministry of Pensions' custody, probably in connection with pension claims, and have been found there.