Cycling is simply trying to produce bacteria and let them established in the tank. Bacteria converts fish wastes(which is ammonia) into nitrites. Then they convert the nitrites into nitrates. Take note that a high level of ammonia and nitrites is dangerous for fish hence we advised you to choose fishless cycling which is cycling without fish.
Without bacteria, you'll find your test kits reading an increasing level of ammonia and nitrites which will eventually kill your fish.
If you cycle with fish, then you have to test the water parameters daily and if you see a spike in ammonia and nitrites, do a water change.
When doing water changes, there is no need for you to remove the fish.
Simply remove a partial percentage of the water and replace it with new water straight from the tap. Before you place the water in the tank, treat it with dechlorinator to eliminate chlorine and chloramine which are harmful to the fish. Goldfish
won't thrive long in a 19 liters tank. You'll need 50 gallons for two alone. They can produce wastes a lot meaning you do more water changes than usual which is almost daily water changes.
Test the following water parameters:
Ammonia, nitrites, nitrates, pH
You buy those in a test kit which is often available in your shop.