As a simple example:
1. after place'n'route you have gate-level netlist (.v verilog), which contains std. cells and wires between them).
2. also, you should have spice (transistor-level) netlist (.sp, .cdl or other extensions), which contains transistors and wires for each of you std. cells.
3. you should convert gate-level netlist into spice-like netlist and merge it with std. cell transistor-netlist.
4. the LVS tool extracts transistor netlist from layout (GDSII) and writes it into spice-like netlist .
5. the LVS tool compares your merged tran-level netlist with extracted tran-level netlist.
The extensions of netlist files may vary and depend on LVS tools.