Forms NATF 85 and 86 can be downloaded and printed from your computer in PDF format, or you can order the Civil War records directly through their online service. Due to the heavy load of incoming requests, it will generally take several weeks for you to get a response, so be patient. There is a charge for records that are located and copied for your use.
While you're checking the web, look for state museums and archives, educational information sites, and links to genealogy sites. A good search engine query such as [your state] "civil war" genealog or [your state] "civil war" records may turn up a variety of useful databases and resources, such as the Roster of Wisconsin Volunteers, War of the Rebellion, 1861-1865, and the Texas State Library and Archives Commission Index to Confederate Civil War Pension Applications.
For Confederate records, the best source is the National Archives microfilm of Virginia regiments. After looking at the alphabetical index, you can go to the correct regimental muster cards. These are much like the Union cards but usually not as complete or informative. However, one common record found for Confederate and not Union soldiers is an oath of allegiance, which Confederate soldiers who had surrendered were required to sign before they could return to their homes. These signed oaths can be very descriptive.
There are pension records for both sides, but the Union records in the National Archives in Washington D.C. are far superior to the Confederate records in Richmond at the Library of Virginia. For Union records you can apply to the National Archives using NATF form 85, either online or by mail as discussed above. For Confederate pension records you will want to contact the appropriate repository for the State in which your ancestor lived. Some states even have their Confederate pension indexes online, including Virginia and Texas. The pension records may list family and perhaps discuss wounds received in the service. Many West Virginia Confederates never received pensions at all.

