As usual, you need to reference liabraries System.Configuration to access AppSettings and Microsoft.Sharepoint for sharepoint object model

public void DeleteFile(string FinalFileName)
{
string s_FileName = "";
string doclibname = ConfigurationManager.AppSettings["doclibname"].ToString();
SPSite objSite = SPContext.Current.Site;
SPWeb objWeb = objSite.OpenWeb();
SPFolder mylibrary = objWeb.Folders[doclibname];
foreach (SPFile file in mylibrary.Files)
{
if (file.Name.ToString().ToUpper() == FinalFileName.ToUpper())
{
objWeb.AllowUnsafeUpdates = true;
file.Delete();
mylibrary.Update();
break;

}
}

}