Since there is no ammonia reading and no nitrite reading, that's not why the fish died. You can add a fish to new dechlorinated water (cycling with fish), but you'll have to test frequently, depending on stocking level, to watch for ammonia and nitrite levels. They will start to climb as a result of fish waste and perhaps left over food rotting. You could have just received unhealthy fish.

But as recommended, get the API Freshwater Master Test Kit anyway. It's a vital tool. If your one fish remains alive, just monitor your water every other day - if he's the only fish in there. If the ammonia level climbs above .25, do a water change of 50%. Continue to do this (could be weeks) until there are no ammonia or nitrite reading, and you start to see some (10-20) nitrate readings.