Photography is all about how you play with light. Whatever be the kind of photography you do, light is the essential common denominator, be it portrait, landscape, macro, or any other thing you can think of.
Light trails are a mix of use of depth of field, controlled shutter speed and ISO. Along with the basic trinity, you also bring in creativity, and different props. The understanding of how a shot is being taken, or how it should be taken, is paramount while doing light trails, light paintings and such.
Its not always that a slow shutter is all you need. Sometimes, varying the light source also helps.
In the end, all that matters is, that you must have a lot of fun.
Have fun experimenting with different light sources. Understand this, when your shutter is open during an exposure, any and every movement of the light source pointing towards the camera, shall be captured by it. Use this to make shapes, letters, drawings .. the possibilities are limitless.