Browse lyrics databases like LeosLyrics.com orAbsoluteLyrics.com if you're not sure of the exact title of the song. You can search the lyrics until you find the song you're looking for.
Look on iTunes or Rhapsody.com to see if the song has been digitized for MP3 sales. Many oldies songs are available as instant downloads for only a nominal fee.
Consult your local music store for information about special ordering the album. Even if you can't find the song online, chances are it is still available on a CD.
Visit a record store if you still can't find the song you're looking for. It is imperative that you consult a true "record store" that sells vintage vinyl records, not CDs. The music lovers working at stores selling collector-quality LPs and 45s can track down virtually any record, even obscure titles that were never made available in CD or MP3 format. You may end up paying quite a bit for an old vinyl copy of the album, but it is worth it to get your hands on your favorite classic song from yesteryear. Additionally, in some cases you'll be pleased to find low-cost replicas of older LPs, becoming increasingly popular since vinyl's comeback---according to an ABC News article, the Recording Industry Association of America reports that old-fashioned LPs have been making a comeback since 2007.