Hi there and welcome to the beginners section!
In my opinion you are very lucky to have stumbled into our section while your fish are still alive! You've at least got a chance now of saving them. Without anyone helping you understand what the "Nitrogen Cycle" is and without your tank yet having a working "biofilter" (we'll explain that) the situation could be a lot worse very quickly.
First things first - you are indeed now in what we call a "Fish-In" cycling situation. The most urgent things you need to learn first are how to do water changes with good technique and then to quickly read and come up to speed on the reasons behind the urgency. The power of a good water change is rarely understood by someone new to the hobby and since it involves effort, rather than fun, its downplayed or rarely mentioned at a pet shop.
The main tool needed for a good water change is a thing we call a gravel-cleaning-siphon. Its just a clear plastic cylinder, sized to be reasonable for your tank size and height and it feeds into a long siphon hose of some sort. This is used to siphon water out of your tank and into the garden or a drain or a bucket so you can carry the water elsewhere. Whenever you remove water you always use the cylinder to plunge down into the gravel and cause it to be stirred up and release the debris that has collected there because of gravity and the lack of water flow in the gravel. This debris and the water around it will contain greater amounts of substances you want to remove with a water change.
Since your tank is new, the tank water chemistry will be nearly identical to the chemistry of your tap water or whatever you used to fill the tank. This is good because the fish will not have become acclimated to something else, like water with more concentrated minerals or metals. So you'll be able to safely do quite large water changes without harm to the fish. And indeed this will be what's needed in a fish-in cycle situation, large percentage changes like 50 or 70% of the volume.
When refilling the tank you need to use "conditioner" to remove the chlorine or chloramine that your tap water was probably treated with to lower the bacteria count for humans. With a new tank in its first year its better to dose this conditioner at 1.5x the amount the instructions tell you, but don't go over 2x the amount while you are cycling. The other important treatment for the return water is to somehow make it roughly match the tank water in temperature. You can use your hand to judge the temperature matching. That's good enough. I have a normal fiberglass lined hot water heater tank, so I just mix hot tap water with cold tap water to match the temp but in some situations people use kettle heated water because they are worried about metals in their hot water heating system.
OK, so that covers good water changing technique, but why worry about all this? That's where your homework reading assignment comes in: read the "Nitrogen Cycle", "Fish-In Cycle" and perhaps a few other articles in the "Cycling" section of our Beginners Resource Center at the top of the "New to the Hobby" forum here. That should give you the background about the toxins that fish give off and that quickly build up in their tank water if they don't have a functioning biofilter. It takes generally a couple of months of work before a filter is ready to handle fish, so its safe to say that you don't have one of those yet! Instead, its going to be -you- that will have to behave as a "manual" filter, removing and adding fresh water by hand as a way of filtering the water and diluting the toxins.
The other crucial thing you'll need will be a liquid-reagent-based test kit. Many of us like and use the API Freshwater Master Test Kit but there are others that are ok too. Once you get one you should post up your tap and tank results here for the members to see. Probably you'll have plenty of other questions as you read the articles and get started too!
~~waterdrop~~