Start every day with a brainstorming session. Don't think about what you are writing, just write for ten minutes without stopping. This may be hard at first, but with practice, it will become easier.
Analyze your brainstorming session and on a separate sheet of paper, write down any ideas that look interesting to you. Memorize the list of ideas so that you can continue to work on the lyrics when you have down-time.
Pay attention to ideas as they come to you throughout the day. If you have a good idea, pay attention to it, but don't write it down yet. Spend some time thinking about the idea. If the idea is a good one, you will still remember it the next day.
Keep a journal to write down your ideas. If an idea stays with you for more than a day, write it in the journal to develop it at a later time.
Sit down at some point each day and work out your lyric ideas that you created from the brainstorming and journal sessions. Don't worry if the lyrics rhyme, proportional lines are more important than rhyming for music. While it isn't your job to set the lyrics to music, try to use words that begin with consonants as they are easier to hear when sung.
Learn about the habits of professional lyricists and writers. Most professional writers will sit down at the same time each day and write for three to five hours. You must set time aside each day if you want to be a professional lyricist.