It is an indisputable fact that dance and music go hand in hand. With the exception of some forms of modern dance in which choreographies are sometimes performed with no musical accompaniment, a good musical score forms the basis of a compelling choreography. Look for inspiration through music, and allow the music to guide your choreographic process by allowing the emotions the music stirs within you to manifest in your movements. It has been said that the revered ballet choreographer George Balanchine used dance to "create musical visualizations" on stage.
Many choreographers, particularly those who work mostly in the contemporary dance field, use improvisation to create choreographies. Often using improvisational input not only from their own ideas but from those of their performers/students, choreographers look to the improvisational technique to create a dance piece that allows the natural movement of the body to present itself and then be manipulated so that all members of a dance group may perform it. Improvisation allows dancers and choreographers to discover the boundaries of their own bodies and thus create original choreographic works.
The use of a theme to inspire ideas for choreographies is a surefire way to come up with an abundance of creative ideas. Options for themes are nearly endless, and your choice of theme should reflect the type of dance style you are choreographing. Some ideas for contemporary dance choreography themes include famous paintings or poems, where dancers interpret the visual and written content of each through movement. When creating choreographies for younger students, consider choosing a theme they can relate to, such as a popular movie or character theme.
Believe it or not, inspiration for dance choreography can be found by simply observing the interactions of people around you in everyday life. Most dance choreographies try to tell a story, and the stories of people and their relationships to others, places and things are the most natural stories on earth. Try sitting in a park for a few hours and observing different elements. Perhaps you will witness a lover's quarrel that will inspire a thematic choreography based upon love and hate; perhaps you will witness a child relentlessly chase after a pigeon and will be inspired to devise a choreography based on innocence. The possibilities are endless.