Micronized (very finely ground) lime will begin to neutralize acidity pretty much immediately. The hydrogen ions (H+) are the primary cause of acidity, H+ is a cation so it is attracted to the negatively charged 'exchange sites' of materials like peat, humus and clay. Humus and clay are denser, heavier materials which have more exchange sites in terms of volume and thus higher CEC. The higher the CEC, the more lime which is typically required at once, though less frequently. Materials such as sphagnum peat, on the other hand, require less lime but more frequent applications. CEC varies drastically even between batches of peat, but peat is a good example because it harbors loads of reserve acidity which absolutely necessitates liming.
The acid (H+) breaks the calcium away from the carbonate (CO3), which goes on the react with the H+ to yield carbon dioxide and water. Calcium ions (Ca2+) are also positively charged, and are thus cations which are attracted to the exchange sites of materials like peat, humus and clay.