How is gravity produced on a spaceship?

Gravity is a property of all material bodies and cannot be directly "produced". Since the magnitude of the gravitational force depends on the mass and distance of the bodies acting on each other, we can make a smaller model of the Earth with the same gravitational effects on its surface. From Newton's law of gravity, it can be calculated that if we had a spaceship with a radius of 1 km (I'm just guessing, I don't know the parameters of the Empire's ships off the top of my head ?), it would have to have a weight of about 1,016 kg. That's quite a lot of material that would need to be transported into space.

Another option is to replace gravity with another force. In order to move on a spaceship, we need to be attracted to it by (any) force but we don't care what the origin of that force is. Therefore, we can replace the gravitational force with centrifugal force — if we make a spaceship circular and let it revolve around its axis, we will have a centrifugal force that will push us to the circumference of the spaceship. By choosing the appropriate rotation period, the centrifugal force will achieve the same magnitude as the effect that gravitational force has on us on the Earth. You just need to realize that we would be walking "upside down" — i.e. on the outer shell of the station and also that due to the small size of the spacecraft, the resulting "centrifugal" field would not be homogeneous (but the gravitational field would be equally inhomogeneous). Such a space station should have a spherical shape and at the given dimensions, it would rotate with a period of about 1 minute.

In both cases (heavy body or rotation) it is necessary to realize that due to the very small size of the spaceship there would be large differences in the value of gravitational/centrifugal force at different distances from the centre of the ship. Therefore, such a spaceship should ideally have only 1 floor, or maybe more precisely one deck. For example, at a depth of 500 m, the gravitational/centrifugal field would be 1.4x stronger, so an 80 kg person would feel like they weigh 110 kg!