Open your image
Open up shot(s) of fireworks and night scene in Photoshop.
Move your fireworks
Select the Move Tool and drag the firework image on to your night scene. You should now have two layers: your original image and the firework shot visible in your layers palette.
Make your firework fit
It's unlikely your firework will fit perfectly so with the firework layer selected, go to Edit>Free Transform. This will apply a box, joined by several anchor points to your image which you can use to resize the shot to fit. By pressing the shift key on your PC's keyboard while making the adjustment, it will stop the shot distorting. Once you're happy with the size adjustment, hit your enter key to apply the changes. If you want to move the firework to a different part of the sky, make sure the Move Tool is selected and click and drag the firework to where you want it to be.
Get rid of the background
The firework's in our sky but at the moment it doesn't look like it belongs there, that and some of the sky is sat across the monument in our shot. To fix this, double-click on the firework layer in the layers palette to open up the Layer Style options.
Once it's open look to the bottom where you'll find a box which
says 'Blend if'. Make sure Grey is selected in the drop down menu and drag the black marker on the 'This Layer' slider until the background the firework is sat on vanishes. Don't drag it too far to the right as your firework will vanish as well as the background. If you plan on adding more than one firework shot to your new scene you'll have to make this adjustment to every shot.
If you need to further adjust the firework so it looks like it's sat in the night's sky, adjust the layer's opacity.
Repeat the process
Then you just have to repeat the above steps with each firework you add to your scene until you're happy with the display.
Here's another shot we added fireworks to: