In PvP, Dominixes are typically flown solo PvP or in small fleets (often, if in small fleets, using remote repairers to support each other).
The Dominix is also used for various kinds of PvE combat. It can run nullsec anomalies where the drones automatically aggro the NPCs, but it is also a popular choice for running Level 4 missions. The Dominix outcompetes the other Tech 1 drone battleship, the Armageddon, in this role, as it has bonuses to drone tracking and range that the Armageddon lacks.
As most of the ship's DPS stems from the drones, the high slots can be used in many ways. Turrets can make a Dominix into an absolute DPS machine. With no bonuses for a particular turret type, projectile turrets are a popular option, as they use no capacitor and allow damage selection.
Remote reps are a popular high slot choice for small groups of Domis, which can then collectively repair whichever member is targeted. Energy neutralizers for capacitor warfare are obviously also helpful. A drone link augmentor can usefully increase the drone control range.
The Dominix is also flexible in its tank. It is most commonly armor-tanked, either buffer or active. It also has many hull hitpoints, making a hull tank viable. In some cases Domis are even shield-tanked.
PvE
Domis in missions often use sentries and an MJD to snipe the NPCs from a distance, but fits based on heavy drones are also viable.