For routine water changes one you have cycled, you would leave the fish in the tank while you siphon out some of the old water (25-30% would be normal unless you have ammonia/
nitrite issues, in which case you would want to change 50% at a time). When you put new water in, be sure that 1) the temperature is as close to the same as the existing tank water as you can get it, and 2) that you treat the water for
chlorine/chloromines before putting it into the tank.
Since the tank is new, you are looking at approximately 4-6 weeks to cycle it using ammonia before you add fish. If you are wanting to speed that up and are willing to plunk down a few bucks, Bio-Spira that FLBettaCouple mentioned will do it virtually immediately...you add the Bio-Spira, then your fish can go in right away.