The short answer
Add new fish without stress by quarantining them first, acclimating them slowly, and introducing them a few at a time. Rushing any of these three steps is what shocks fish — sudden changes in water chemistry, an undetected illness, or too many newcomers at once. Take it gradually and both the new arrivals and your existing fish stay calm.
Quarantine first
Ideally, new fish spend two to four weeks in a separate quarantine tank before joining the main aquarium. This does two jobs: it lets any hidden disease show itself where it can’t infect your whole tank, and it gives stressed, freshly-shipped fish a quiet place to recover and start eating. If you can’t run a quarantine tank, at least buy from a reputable source and watch new fish closely for the first fortnight. See do I need to quarantine new fish.
Acclimate slowly
Fish are sensitive to sudden shifts in temperature and water chemistry, so never tip a bag straight into the tank. Float the sealed bag for 15–20 minutes to match temperature, then add small amounts of tank water over the next 20–30 minutes so the fish adjusts gradually, and finally net the fish across rather than pouring in the shop water. Our step-by-step acclimation guide covers the full method.
Add a few at a time
Don’t restock a whole tank in one go. Adding lots of fish at once overloads the filter, spiking ammonia before the beneficial bacteria can catch up, and it disrupts the existing pecking order. Introduce fish in small batches, and rearrange the decor before adding to a tank with territorial fish so nobody “owns” the space yet. Keep the lights low for a few hours afterwards. For why all-at-once is risky, see can I add all my fish at once, and check the tank is stable first with a test kit.