A very simple description of an FPGA is that it's got a bunch of switches on the ends of wires. Some of the switches can connect wires to logic elements and some can connect wires to other wires. In this view, programming an FPGA is just toggling switches so that some of them are "on" and the rest are "off".
The easiest migration from FPGA to ASIC is to just make a chip with the same circuit elements and wire segments, but instead of making switches, you just short out connections in the "on" state and leave the rest open.
