There are a total of 12 keys in music theory. Songs (or parts of songs) are often referred to as being in a certain key, which describes the relationship between the chords used and the tonic, which names the key.
The most common chord progression in popular music is the first, the fourth and the fifth chord in any given key. In C this would be C-F-G. It is important to remember that the relationship between the first and fifth chord is very powerful, and that the seventh chord in a key is rarely used.
All keys have seven notes and follow the pattern of whole-step, whole-step, half-step, whole-step, whole-step, whole-step, half-step. In the key of C this gives us C-D-E-F-G-A-B. The melody to a song can be crafted simply by playing notes within the scale until something sufficiently "catchy" or desirable is developed.
An important aspect of writing modern songs is structure. Even if the constituent parts of a song are compelling, structuring them in a predictable or cliché manner could lessen the impact felt by the listener. Simply modifying or displacing any step in the traditional verse-chorus-verse format could greatly enhance the appeal of a song.
Music theory provides a framework for writing songs, but the rules of theory can be broken. Key changing and using chords outside of the established key of a song are simple ways to craft more unique and compelling songs.
Lyrics are an important element of modern pop songs. The most accessible songs feature many repeated lines that apply to a wide group of people, which broadens the appeal of a song.