Search for the album name via a search engine like Google, Bing or Powerset. Type in the artist's name or the title of a song from the album into the search engine. This will likely take you to the band's or artist's homepage or a discography. You can then sort through the albums listed to find the one you're looking for. You can also use a discography database like Discogs.com to search for the album name.
Search by lyric. If you don't even know who recorded the album you're looking for, you might think you're stuck. Not true. As long as you know even a portion of the lyrics, you can still search for a song, which will then lead you to an artist and album. AZLyrics.com, Lyrics.com and MetroLyrics.com are three of many song lyric databases that make it possible to search for a song using the lyrics.
Ask a professional. Go to your local CD store and ask the people who work there if they know the name of the album you're looking for based on the song title, artist or lyrics. Or you could even email or call a pop, rock, rap or alternative radio station to ask if they know who recorded a particular song and what album it's on.
Use technology. A song-identifier software program like Tunatic, Tuneup, Simplify, Shazam or Midomi can help you identify a song's name, the artist singing it and the name of the album it's from by "listening" to the song and searching its database for the song information. Some identifier programs can be downloaded as applications onto your smartphone. Others are available through music-streaming programs like Pandora and iTunes.