Take a sphere for example and animate it scaling outwards uniformly. To simulate drag, set the timing of the scale to slowdown over time by using either bezier function curves or TCB controls. Add some fractal displacement to the sphere to breakup its profile over the course of the explosion. By using layers of self-illuminated fractal noise maps you can get a somewhat convincing fiery look. Control the speed at which the fractals move to help convey scale.
Particles are another tool useful for making explosions.
Many packages have particles integrated into the toolkit that you can use to create blasts of polygons or points. The important thing here is to break up the edges of the facings with another noise map or gradient. Mixing up the particle types is another way to do this. Some packages let you use spheres or tetrahedrons as well. Variation in the particle velocity is important too.