¶ Summary
Although drones offer fully-selectable damage, the Dragoon is not typically used for PvE combat, because its hull bonus to energy neutralizers is useless against NPCs. However, the Dragoon's 5 high slots, makes it a good potential PVE ship with salvage capability while keeping its full complement of launchers or turrets.
¶ Skills
Like other Amarr ships, the Dragoon lives by its capacitor, and capacitor skills—notably Capacitor Management and Capacitor Systems Operation—really help it, as does the skill which reduces the capacitor burden of energy neutralizers, Capacitor Emission Systems. It's good to have these trained to at least IV.
¶ Tactics
Another is using nosferatu modules to recharge energy from any larger enemy ships nearby. Since a nosferatu transfers capacitor to your capacitor if you have less raw capacitor than your target, not if your percentage of capacitor is lower, the Dragoon can run its own capacitor off the energy of an opposing cruiser or battleship for some time. A third help can be giving up one of the Dragoon's sparse mid slots for a capacitor booster. Advanced pilots can also consider the Mindflood combat drug: none of this drug's potential side-effects inconvenience the Dragoon. If its own capacitor can be sustained, the Dragoon can "cap out" other destroyers and cruisers.
With T2 drones and decent support skills, the Dragoon's drones can make short work of most frigates too slow to outrun them, and can add DPS to a gang's efforts against larger targets.
In PVE, the Dragoon's relatively low tank limits its ability to take on particularly large targets or large combat sites, but a capsuleer can with relative ease take on level 3 combat sites by taking advantage of the drones and extending their control range letting you kite out of range of missile batteries and other defence platforms. The extra 2 high slots lets you use these for quicker salvage instead of capacitor warfare.