To use warheads, you also have to research some kind of missile (in the tech tree in the game I'm currently using, cruise missiles are available first).
After you research that kind of missile, you can mobilize missile launchers, which are ground-based units that can fire the missile once every few hours (it depends, based on the kind of missile). When you fire a missile, you expend either 1, 2, or 3 warheads (depending on the kind of missile), and the warhead impacts the target, damaging it. You can also research and mobilize other units capable of firing missiles, like strike fighters, bombers, SSBNs, and destroyers, which give you more flexibility in terms of where you want to launch your missiles from.
"The enemy cannot push a button, if you disable his hand."
Sergeant Zim, Terran Federation