Use of the word gravity here simply refers to the apparent effect, not the underlying forces and principles involved. Oddly enough, because of this, most people do not realize how important an atmosphere (any gas/plasma) is in an artificial gravity situation. Imagine this scenario:
A cylindrical craft is launched and begins an interplanetary voyage. If there is a clear area on the inner circumference of the craft, a suited astronaut (before the craft has started rotating) could evacuate the atmosphere, place himself at a stationary point inches from the wall in this area and then have the craft begin rotating. The astronaut would simply remain floating inches from the spinning wall.
The reason for this is simple. This type of artificial gravity relies on the exact same principle as the rocket did to take off and accelerate. Transfer of Momentum. The rotating craft has a certain amount of energy invested in it by the rotational thrusters. In a vacuum (inside and out), there is no medium that can transfer this energy to any other object that is not in direct physical contact with the rotating portions of the craft. No transfer, no movement. Any particle that has energy and can interact with matter can transfer momentum. And a gas, while not the most efficient means, has an big advantage in that it occupies a larger volume at a given density than a solid.. Each gas atom that contacts the spinning wall, picks up momentum. Each gas particle that collides with an energized one transfers a portion of that momentum. The end result is that the craft loses a little momentum to the air, which in turn, is now imparting that momentum to any object it comes in contact with. And since the momentum in any portion of the rotating craft will be towards the closest wall, you will move in that direction faster and faster since the gas will get denser the closer you get (remember, the momentum the gas has will cause it to move towards the wall as well which raises the density) and the more gas particles impacting you, the more momentum, and the faster you move. In a small craft, the density changes would be negligible and your rate of fall would not perceptibly change before you contacted the wall. In a large craft (such as a hollowed out asteroid tens of kilometers across, the pressure changes would be such that there will be an area in the center where pressure drops towards vacuum and apparent gravity to zero (no gas to transfer momentum). Incidentally, a small craft will require more frequent rotational thruster bursts since the amount of energy invested in the craft is negligible, and momentum will be bled off quickly by friction in the internal atmosphere. A large craft has so much mass invested in in the craft itself, that the momentum bleed off will negligible.
Once you've contacted the wall, you will acquire the same momentum it has. In order to leave the wall, you would need to somehow shed this energy in order to get airborne. I suppose if the craft is large enough, you could employ a lift or ladder, but on a small craft, there will not be enough pressure change to create a central vacuum to float in.
Please note that I left out the whole sideways vector responsible for most of the problems people would experience in a small rotating craft to simplify the explanation.