Listen to lyrics you think are good. Like any art form, it's important to study the masters, the people you consider to be talented lyricists. Read over the lyrics and try to think why they impress you. The reasoning can vary based on your interests. Are the lyrics catchy? Fun? Share an emotion? Tell a story? Are clever? Move you emotionally? Help you learn about someone? Discuss an important part of life? Identify what makes these lyrics good, and you'll better be able to write your own lyrics.
Think of a subject on which you want to focus your lyrics. Some common subjects include love, heartbreak, and desire, but you're certainly not limited in what you can write about. One of the keys to writing good lyrics is writing about what matters to you.
Write down lyrics. Don't worry about what you're writing, but simply write down lines. You can always cut out words later. As you write, try to be honest. Listeners typically look for emotions in good song lyrics, so try to open yourself up to your feelings and honest emotions.
Add rhymes if you want. A lot of lyrics rhyme, typically at the end of the line, but you don't have to have rhyming lyrics to be a good lyricist. However, rhyming lyrics is a way to make them become easy to memorize for listeners, and can also help make them catchy. Consider Sheryl Crow's hit song, "All I Wanna Do." In the chorus, she sings this rhyme multiple times: "All I wanna do is have some fun/I got a feeling I'm not the only one."
Look over what you've written. Pay attention to the length of the words and lines. Do they flow well together? Are there words that awkwardly stand out or are perhaps too many syllables? As well, are there lines that could be repeated, to make a memorable chorus? Are there words or lines you think would connect with listeners? If they feel connected to what you're singing about, this will increase their interest in your lyrics.
Keep writing song lyrics. Like anything, persistence and continual practice is what can lead to getting good. Lyricists typically write a lot of lyrics, even before they have any success. Continue to follow these steps and after awhile you should have some lyrics you're proud of and may resonate with others.