The main processes involved in lithification are compaction and cementation. Compaction involves squeezing the sediment into a smaller volume by packing the sediment particles more closely, by removing water from the pore space (desiccation) or by pressure solution at the points where sediment grains contact each other. Cementation involves filling pore space with solid minerals (usually calcite or quartz) that are deposited from solution or that enable existing sediment grains to grow into the pores.
The pore space does not need to be eliminated for lithification to be complete. All of the processes of lithification can continue to modify a rock after it has first become a rigid solid.
Lithification occurs entirely within the early stage of diagenesis. Other words that overlap with lithification are induration, consolidation and petrifaction. Induration covers everything that makes rocks harder, but it extends to materials that are already lithified. Consolidation is a more general term that also applies to the solidification of magma and lava. Petrifaction today refers specifically to the replacement of organic matter with minerals to create fossils, but in the past it was more loosely used to mean lithification.