There are two things that could have killed the fish - ammonia or chlorine.
Dealing with the ammonia possibility first, fish produce ammonia as part of their respiration process. Ammonia is highly toxic, it burns their gills, restricting their ability to take in oxygen, and once in the blood stream it does all manner of damage to their internals as well. In the wild, the water in their lakes and rivers is constantly refreshing so it doesn't matter. In an enclosed fish tank, there is nowhere for that ammonia to go. The good news is that there is a family of bacteria which love to eat ammonia, and these will start to grow in your tank, mainly in the filter but also in the substrate.
The downside of this is that these bacteria produce nitrite. Nitrite is also highly toxic, it attaches itself to the fish's haemoglobin, and stops it from transporting oxygen around the body, effectively it suffocates the fish. The good news is that there is also a family of bacteria which love to eat nitrite, and these will also start to grow in the filter and substrate. These bacteria produce nitrate, which, in low quantities, isn't toxic at all.
This is the nitrogen cycle. Growing the bacteria colonies in your filter is called "cycling". You haven't yet achieved this, but you will.
To do this properly and safely, you must (and I mean MUST) get your own liquid test kit. You need to test your water every day, and change enough water to reduce the ammonia and nitrite levels down to about 0.1ppm - this is too low to be measured on most hobbyist test kits, but will still provide enough ammonia to grow the bacteria. To decide how much water to change, it's basic maths. If you see a level of 1ppm, then to reduce this to 0.1ppm, you need to change 90% of the water (1-0.9=0.1). If you only have 0.5ppm, then you only need to change 80%. If you see 2ppm, then you need to change 95%. In practical terms, this would mean 2 water changes of as much as you can, in quick succession.
If you don't see a reading for either ammonia or nitrite, then you don't need to change water.
Initially, you will be changing water everyday, because you will be doing the bacteria's job for it. As time goes on, and the bacteria grow, you will get to a stage where you'll only need to do water changes every two days, then every 3, etc. Once you get to a stage where you can go a week without having to change water, you are classed as "cycled", in other words, you have bacteria colonies large enough to deal with the ammonia produced by your current level of fish.
At that point, if you wish to, you can add additional fish, such that you are adding another 25% to the bioload. This is an inexact science, but if you had 4 guppies, you could add another one. But you could potentially add 2 much smaller fish. (This obviously depends also on your tank's capacity). Because there will be more ammonia being produced, the bacteria colonies will need to grow to cope, so you will need to go through the above again, although it will take a LOT less time - we call this a "mini-cycle".
At the moment, though, you don't have a test kit, so I would say you need to do daily 80% water changes until such time as you can buy a kit. I personally recommend either the Salifert or the Nutrafin tests. Many on here use and recommend the API kit, but there are significant issues with both the ammonia and nitrate tests, so I don't use that range. So long as you get a liquid kit, rather than paper strips or tablets, you won't go too far wrong.
You may be wondering why your fish shop tested your water, and told you it was fine to add fish, when I've just told you that you have a problem. When the shop staff test the water, they are looking for the presence of ammonia and nitrite. But there was nothing in your tank to produce ammonia or nitrite, so at that stage, the water itself was fine, it was the filter that was not ready.
Now, about my 2nd possible cause of death. You said you hadn't used any chemicals at all, and I am assuming this includes water conditioner, aka dechlorinator. As you'll no doubt know, your water company adds chlorine (or chloramine) to the water to destroy any nasty bacteria and make it safe for human consumption. When it comes out of your tap, it's at a concentration that won't hurt you, but it is also a problem for fish, and immature bacteria colonies. We use dechlorinator (I recommend Prime, as do most on here) to remove chlorine and chloramine, and also to remove any heavy metal pollutants in the water. Since it seems you haven't used a dechlorinator, it may well be the chlorine/chloramine that killed your fish.
Even if the latter was the issue with your tank, you still will be having the former problem, so this is all stuff you need to understand. Sorry it's so long-winded. If you have any other questions, however silly you think they might be, please ask them, we were all beginners once.