Some people like to write the lyrics first, and some prefer to write the lyrics after they have written the melody. If you write the lyrics first, you’ll need to write the melody to fit the lyrics, and if you write the melody first, you’ll need to write the lyrics to fit the melody. Both ways have their advantages, and as you gain experience in song writing, you’ll find the way that works best for you. But whether you write them first or last, there are a few things you’ll have to know.
The ballad stanza is the most popular lyrical form in English for songs and has been for a long time now. The ballad stanza consists of four lines, usually rhyming ABCB, but sometimes rhyming ABAB. Here’s an example from Bob Dylan’s "Blowing in the Wind": "How many roads must a man walk down / Before you can call him a man? / How many seas must the white dove sail / Before she sleeps in the sand." This sort of stanza is often used in the verses, and there are frequently two such stanzas per verse. It can also be used in the chorus and bridge.
There are several other forms that you can use: the couplet (two lines that rhyme); a ballad stanza followed by a couplet; two tercets (stanzas of three lines each); etc. Generally, the number of lines in a verse, chorus, or bridge is even. The lines can rhyme (or not rhyme) any way you want them to. The lines themselves should be more or less regular metrically. That is, the lines should have about the same number of syllables and the stresses should be in the same places (but you have a lot of freedom in determining what words will be stressed). The reason for metrical regularity is that you only have a certain amount of time to sing the line in, and every line will be sung to the same melody. The melody, however, is often varied slightly to accommodate the lyrics.
Remember, lyrically the verses are different, but the chorus is the same. The chorus repeats the same lyrics over and over again throughout the song. Obviously, your chorus needs to be strong to bear that much repeating. Often (though by no means always) the verses will tell a story while the chorus repeats the theme or the emphasizes some aspect of the story. The chorus will always be relevant to the verse that precedes it, and though the lyrics of the chorus never change, the meaning can change subtly throughout the song as the verses reveal more information. The chorus will sometimes change slightly (by a word or two), and this change often occurs in the last chorus, where the lyrical content of the song resolves itself—this technique is very popular in country music.
As with the melody, there are no hard and fast rules for writing the lyrics. You are the final judge as to whether the lyrics are "right" or not.