For the MPLMs that were carried up by Shuttle, everything was packed in soft-ish fabric bags strapped to the walls. A lot of custom cut foam was used to secure the items. So when you opened one of the bags, you'd see foam, and you had to pull all that out to get the items. Typically this foam would go back down as garbage.
The bags can be custom sizes for large items.
An aisle is left down the middle for access, as shown in this picture of Sandy Magnus inside the MPLM that STS-135 took up. (this MPLM is probably partially unpacked)
Since the Cygnus is basically an MPLM, I imagine it is the same. No personal knowledge of Dragon, but it sure looks similar:
Finally, how is it unloaded - by hand. On shuttle flights one of the mission specialists was designated the Loadmaster who kept up with and directed the unloading, unpacking, and reloading.
There is a funny (if somewhat sexist) shot in one of the NASA IMAX movies (I think Space Station 3D) where the male crewmembers "unload" Marsha Ivins as though she were cargo and pass her up through the hatches just like the other items of cargo.
Loading the cargo into the MPLM was no picnic either. In this picture I took in the SSPF, you can see the MPLM is in a cradle that lets it rotate on its long axis. The white cabinet thing that blocks our view into the MPLM controls a movable access arm that allows workers to get in and reach any part of the MPLM to attach the cargo.