Observe the world around you. Soak in the sights and sounds. Listen in on conversations, read billboards and watch TV. Something someone says in line at the bank could be the inspiration for a song title. The sound of a car passing by might inspire a drum beat for a song.
React to the stimuli in your environment. If something someone says hurts you, allow yourself to feel the pain, anger and spite. A real emotion can serve as a solid basis for a song and is something that the average person will be able to relate to.
Channel your emotions into something tangible, be it via music, lyrics or both. If you're feeling happy, try humming a pleasant melody or writing words that express your happiness either specifically or metaphorically.
Devote time to songwriting and listening to music. Flexing your songwriting muscles by setting aside time to work on songs and listening to music on a regular basis will keep ideas in your head, leading to more opportunities for inspiration to strike.