Decide which common song structure your song will have. You may have already made this decision arbitrarily. AAA is three verses back-to-back, with no chorus. Verse-chorus alternates between verse and chorus. AABA is the most sophisticated song form, having three verses with a bridge. A good example of AABA is "Somewhere Over the Rainbow."
Keep the idea, emotionality and purpose of the piece consistent with what you created in the first verse. You can start the second verse exactly the same but change a few words, or you can start with a whole new phrase.
Write the chorus if your song-style requires one. The chorus is where the main idea and hook of the song are most clearly expressed. If you're having trouble thinking of what to say in your second verse, writing the chorus can help guide your decisions.
Give the second verse the same structure, rhythm and key as the first verse. You need to remain consistent from verse to verse. The chorus and bridge can vary in key and tempo so as to bring more attention to those parts. The second verse should look like and feel like the first so that the audience knows you're telling more about the subject and going deeper into the meaning.