It's actually much easier for the crew to enter the vehicle and sit down when horizontal than when the vehicle is stacked and in the vertical position (no climbing up over the MS1/2 seats to reach the commander and pilot seats). For the CEIT the logistics are quite simple. In the OPF then have movable platforms with staircases (similar to what you use to provide stairs for airliners at airports without jetways). Though instead of being just one set of stairs that lead to the door that sticks out perpendicular to the craft, the mobile platforms used in the OPF have a deck that fits along side of the shuttle to provide access to the side of the vehicle instead of just providing a way in/out of the side door.
For the suited crew, the crew just walks up the stairs and through the door into the vehicle. The ascent/entry suits allow plenty of mobility for walking and moving around. The Pilot and commander still have to climb over the C3 panel to get to their respective seats, but that too has a small temporary step placed to assist them up and a cover over the top of the C3 panel to prevent damage to the panel and switches.
There were always a number of pictures taken at the CEIT, (as well as for general vehicle processing in the OPF) so I wouldn't be surprised if you could find a picture of the actual mobile stairs/platform used somewhere on the internet. It will be the same platform that allows the workers is the OPF to access the side of the vehicle for inspection and repair during normal orbiter processing (without having to use an extension ladder with tennis-balls over the tips...)
Ingress to the vehicle when it is stacked and vertical is the same whether it is in the VAB or out on pad 39 A/B. In the VAB you have a "floor" where the floor at each level extends out and fits close to the side of the stacked vehicle providing worker access at just about each level. On the pad you have the walkway that extends over to the orbiter side door (the enclosed walkway you see the crew using to get into the vehicle on TV).
I don't know of any time the crew actually enters the vehicle in the VAB, but they can certainly walk out and inspect how readying for flight is going at any point in time. Getting in for flight at the pad utilizes a number of temporary steps and platforms that the close-out crew provides to help get the pilot and commander in their seats before getting any mission specialists strapped in. The pilot and commander have to enter the door and physically climb up to their seats using the temporary platfoms. The mission specialists are more or less at the level of the door, so their climb into their seats is more or less a horizontal translation from the door into their chairs.
At any rate, there is much more involved in getting the crew into their seats when the vehicle is vertical.