Typically, I get an idea for some lyrics first. They are usually about love or God.
Once I start to get the idea for lyrics, I grab my guitar. (You can, of course, use whatever instrument you are most comfortable with.)
If you do not play an instrument, either find a friend who does, or just stick to the lyrics.
The reason I get my guitar before I finish writing the lyrics is because it helps me create a good flow with the lyrics. It also keeps me from writing the lyrics to a different tune, and then having trouble creating a tune of my own.
Usually, when I have a lyric idea, I also get a tune idea. I either go by ear, or use a tuner, to figure out what notes I am singing and base my chords off of that. Sometimes, however, I do not yet have a tune in mind, so I play around with some chord progressions while saying the lyrics until I start to develop a tune.
Make sure the song is in your vocal range. I am lame so I usually use similar chord progressions and then just throw a capo on in different places.
I usually work with my guitar while writing all the lyrics. I like to structure my songs in this way:
Verse, Verse, Chorus, Verse, Chorus, Bridge, Chorus
The song does not have to rhyme, however that typically makes it more catchy. I usually do very well coming up with the first two verses, then the chorus and second verse gives me a bit of trouble. The bridge usually comes easily for me.
Try not to use the same chord progression for your entire song. Make sure the chorus and verses flow together, though.
Play the chords and sing while you are right, that way you get a good beat and flow. If you come up with the lyrics first, you may need to adjust them a little later to change the number of syllables. Usually, all you need is to add or remove a few small words like "and" or synonyms for the same words, you should never have to change what you are trying to say.
Once you think you have the lyrics and instrumentals finished, try singing it a few times through. You may want to change a few things here and there. While you play, observe whether or not your foot is tapping or your head is bobbing. It is important to establish a good beat.
It helps to listen to lots of music to get ideas.
If you would like to listen to mine, go to www.simplyiyla.com