State governments maintain records and have published compilations of those records. These can include rosters of Regiment and Company, and will often have mustering in and out dates of soldiers along with notes about the service of the regiments. Iowa includes an alphabetical index of soldiers, which can greatly speed up a search. Roster and Record of Iowa Soldiers in the War of the Rebellion Together With Historical Sketches of Volunteer Organizations 1861-1866, published by the Iowa State Assembly in 1908, is an excellent resource. The Iowa Historical Record also contains helpful articles specific to Civil War regiments and officers.
Libraries are excellent sources of published references. I searched in the Sutro Library in San Francisco, the Johnson County Public Library in Overland Park, Kansas, and at the library of the State Historical Society of Iowa in Des Moines. All of these libraries had helpful references, and the State Historical Society had many volumes specific to Iowa regiments. Through these references, once I had Lemuel Burnís Regiment and Company and service dates, I was able to piece together a chronology of his travels and battles in the Civil War.
A guide book I found very helpful is Bertrum Hawthorne Groeneís Tracing Your Civil War Ancestor. He lists numerous routes and methods to follow, and I have only scratched the surface of this excellent reference. Anyone wishing to continue this research is urged to start with this book. Grollierís Multimedia Encyclopedia provided helpful background on the Civil War and key battles.