Access a search engine such as Google or YouTube. Click on the main search bar. Type the name of the artist followed by partial song lyric. Scan the first 5-10 search results and look for the bold phrases of the partial lyric in the result. The song will appear with the rest of the lyrics on the link description.
Go to a music database such as Zworks if you don't know any partial lyrics. Select the "Artist" text box and type in the name of the artist. Click the "discography" tab on the next page, and then proceed to click on the first album.
From the album screen, click on the first song and scan the lyrics to see if it is the song you are trying to find. Repeat for each song until the end of the album is reached. Click the browser's back button until the discography screen is reached, then click the next album, and continue searching for the song.
Listen to clips of songs if there is difficulty finding the correct one. Go to Amazon.com and type in the name of the artist to scan the albums on their purchase pages. Click the "Sample" button next to the songs in the albums and listen to the clips to recognize the correct song.