The first thing I did was to remove the front seat, just to give myself a little more working room. The seat is held on by 8 bolts and two brackets, shown below for the passenger side:
Chevy seat bolts
In retrospect, I probably did not need to remove the front bolts, as they simply hold the bracket in place—not the seat directly. The front supports just slide under the brackets. Here is a front support. Note that one side is larger than the other, to accommodate the sloping car floor.
54 Chevy Seat Bracket
The rear bracket bolts directly to the floor. It is shown here on the left, looking from the bottom up. All the parts for the seat were placed in labeled bin and stored on a shelf.