In this tutorial, I am going to explain how to make fireworks with particles.
You should setup particles for smoke effects which is shot into the air,
and spark effects.
For basics of particle, please refer to
Maya Tutorial:basics of particle
The timing in this tutorial is the below
1 - 15 shot into the air, smoke particles are generated
15 - 17 spark particles are generated
20 - 25 a Drag field affects
Settings for the smoke which is shot into the air 
Make a NURBS sphere, set keyframes to animate the sphere shot into the air.
The keyframes are 1 and 15 frame.
It is better if you set the keyframes only on transform Y.
You will duplicate the sphere later and you can move them to X direction easily.

Select the NURBS sphere, and
Particles > Emit from Object
Particles will be generated from the object.

Settings of the Emitter are the above.
Setup the Rate (how many particles are generated in a second)
frame 1 - 10 1000
frame 15 0

Settings of the Particle are the above.

Assign a Particle Cloud material to the particle,
and connect a Ramp texture to the Life Transparency,
then transparency will change at time.
For more detailed explanation, please refer to
Maya Tutorial:basics of particle
Connect a Turbulence field to the particle to move randomly.
The animation at this stage is shown in the above.
Settings for the sparks
Select the NURBS sphere, and
Particles > Emitte from Object
Two Emitters are connected to the object as the above.

Settings of the Emitter are the above.
Setup the Rate
frame 1 - 14 0
frame 15 5000
frame 17 0
Set more than 0 to the Tangent Speed,
then the particles will be generated randomly from the surface.

Settings of the Particle are the above.
Set the Particle Render Type to Tube.

Assign a Particle Cloud material to the particle,
and connect Ramp textures to the Life Color and the Life Incandescence.
By connecting a Ramp texture to the Life Incandescence,
it is possible to make particles lighten at the moment of explosion.
Set more than 0 to the Glow Intensity, then they will seem to shine.
The animation at this stage is shown in the above.
a Gravity field influences the particle.
a Drag field influences the particle.
Settings for the Drag field are the below.

Make the Drag field the child of the sphere.
Set Magnitude value
frame 20 0.05
frame 25 3
Duplicate the particles

Select the sphere,
Duplicate it with option Duplicate Input Graph,
then all of the connected node(Emitter、Particle、Field) will be copied.
You will move the timing of animation.
It finished.

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