There are two different ways of deploying nuclear weapons within Supreme Ruler Cold War. These two ways are either by using them manually, or by using the strategic reserve, which is only available for the Sphere leaders (US and USSR).
Before you are able to fire your nuclear weapons, make sure that you have the option to use nuclear weapons selected. This can be found:
Currently there is a bug when manually deploying missiles to a specific unit (all types, not just air).
If you want to deploy them therefore, make sure you open reserves and go straight to missile reserves before you select the units you want to load missiles onto.
Once you have selected your bomber, here is how you deploy nuclear weapons onto the unit(and this goes for all missiles too):
Then your unit is ready for nuclear weapons deployment!
Then you have to get the launcher within range of your intended target. Once it is in range then you can select the unit, right click on the target and then fire missile. It will fire the weapon if it is within range of the target, and it will only fire 1 Nuclear weapon at a time (per unit selected), so if you want multiple nuclear weapons to hit the target, then either keep giving the order until happy, or use more units.
The AI will use this to attack you in certain cases if the 2 sphere leaders go to war with each other.
Needs filling in at some point, maybe when I use it
If you use the Strategic reserve, the opposite sphere leader may launch a counter strike against you providing that they have weapons AND the platforms in order to attack you, otherwise they will not counter attack.
The AI will not launch nuclear weapons against the player if they are not a sphere leader or if the nuclear weapons that you used were deployed manually. This can be viewed as an exploit by some.
On high Nuke penalty's it can lead to your troops deserting and everybody around the world hating you whereas on lower difficulties, it will have no consequences.