Write what you know. Turn your personal experience into something unique. For example, instead of writing, "I'm sad," write in detail about an experience you recently had where someone hurt you. Incorporate the sights, sounds and smells from that moment into your lyric to help draw in listeners and help them relate to your experience.
Use imagery and comparison. If you're trying to convey a sense of extreme happiness, don't come right out and say it. Let your lyrics paint a picture and represent a feeling or event.
Subvert a cliche. Turn something familiar into something new. For example, in Toni Braxton's "Unbreak My Heart," songwriter Diane Warren took the notion of a broken heart, added a prefix and put a new spin on asking for one's love back. Try doing the same with your lyrics. There are only so many words in a given language. Turn something common into something unexpected using different combinations of words.
Write down everything interesting you see or hear. George Harrison came up with the idea for the hit Traveling Wilburys single, "Handle With Care," when he spotted an old box in Bob Dylan's garage. If you hear something that strikes you or sounds out of the ordinary, make a note of it or record it on your phone. Maintaining a notebook or database of ideas will help when you're starting to write a song or need a lyric to fit a melody.