4-6 weeks for a typical fishless cycle using ammonia drops. Saltwater tanks with established live rock can cycle in 2-3 weeks. Adding live bacteria starters (Dr. Tim's One and Only, Fritz Zyme 7) shortens the timeline by 30-50%. Never add fish to a tank that hasn't completed a cycle - it's the #1 cause of new-tank fish loss.
Cycling means establishing the bacterial colonies that convert toxic ammonia (from fish waste, decaying food) into nitrite (still toxic) and finally to nitrate (relatively safe at low levels). The colonies grow on every surface in the tank - filter media, substrate, decor, glass walls.
Adding bottled live nitrifying bacteria (Dr. Tim's One and Only is the gold standard) shortcuts the establishment phase. Dose per package directions, then dose ammonia to 2 ppm. Most tanks complete the cycle in 14-21 days using this method.
Live rock from an established system already has bacterial colonies. A 60-75% live rock setup can cycle in 5-10 days. The cycle still happens (bacteria die during transit and need to re-establish) but it's dramatically faster than starting from scratch.
Yes but it's harder on the fish - they suffer ammonia and nitrite exposure during the establishment phases. If you must, use only the hardiest species (cherry shrimp, white cloud minnows, or zebra danios), keep stocking minimal, and do daily water changes.
Nitrite-converting bacteria (Nitrobacter) are slower to establish than ammonia-converters (Nitrosomonas). The "stuck" feeling is normal - just keep dosing ammonia to 2 ppm and wait. Adding more bottled bacteria can speed it up.