The chorus may be the most memorable and catchy part of a song, but it needs the contrast of a verse to make it that important. The verse sets up the the chorus. It serves to introduce new lyrical elements in a song. For example, each verse in The Beatles' "Eleanor Rigby" introduces a new development in the lives, and deaths, of its characters. In some song forms, as in the AABA form, the verse even acts as a pseudo-chorus. No matter how your song is structured, it needs to have an effective verse, and you can make it happen with careful consideration of its place in the song.
Build off of a pre-existing chorus or start directly with the verse. If you have a chorus you really like, you can write a verse off of it. This will allow you to work with a pre-established lyrical or melodic feel of a song. If you don't have a chorus, here is the time to establish the foundation of your song. Try starting with a melody or a chord progression. Think about the ways verses you like in other songs work and model your verse after these.
Let your verse tell a story. The chorus in a song acts as its emotional release. For example, the chorus in Taylor Swift's "You Belong With Me" describes her feelings to a boy she likes, that he belongs with her. The verses in the song describe her dislike of the boy's current girlfriend and why she's a better fit because she really knows him. You don't need to write actual prose in your verse, but let it serve as the story counterpart to the chorus' emotional side. The lyrics to a verse, in order to progress your story, usually change each time, according to Pat Pattison's article on "Verse Development." Many songs with three verses consist of two different verses followed by a repeat of the first verse to tie the whole song together.
Write your verse in contrast to the chorus in terms of pitch and melody. As the chorus contains the high point and overall message of a song, it usually contains the song's highest notes. Make the melody of your verse lower than the chorus. If you already have a chorus, work on transitioning from it into a lower pitched verse. If you're starting with a verse, don't let your notes get too high, as you won't be able to sing your higher chorus when you get to it. The notes of your verse should differ from your chorus in terms of how repetitious and long they are. The expressive nature of the chorus usually calls for long, sweeping notes. Verses usually have more words and, in telling a story, should contain more notes in faster succession. Listen to Belinda Carlisle's "I Get Weak" for a good example of this idea.
Recognize the power of the verse in the structure of your song. The first verse is usually the first part of a song a listener hears. It should come fast (usually at around :13 seconds into pop songs) and be memorable enough to pull people in. The chorus may be the high point of a song, but people won't get there if the verse is boring.