Visit the National Archives site and send in a request to get the forms you need. If you want the full pension application file (highly recommended), you need to request Form NATF 85.You can request 5 forms at once.
When you get the forms, fill out as much info as you have on the person you are searching.Keep in mind that there are a lot of soldiers with the same name, so you will need the correct name of the unit.Be sure to check the box for "Full Pension Application File."The cost of the full file (if they find it) is $37, regardless of how big the file is.(I think.)
Then wait.It took several weeks for the files I ordered to arrive, but so far I have received 3 of the 4 files I requested and they are full of useful information.