If you are cycling with fish in the tank :
Make sure you have a good liquid drop test kit. Do whatever water changes are necessary to keep ammonia and nitrite below .25 ppm. Eventually, in a number of weeks perhaps, ammonia and nitrite should be 0 ppm all the time, and Nitrates should increase slowly. Then you will do regular water changes depending on stock together with a gravel vac to keep Nitrates below 40 max (shoot for less than 20).
.6 ppm ammonia is plenty high to kill your fish quickly and in any event cause gill damage which is permanent.
The fact that you already have nitrate would indicate that you have some of each kind of necessary nitrifying bacteria so the cycle should be relatively quick from here.
If you are not cycling you have some problem which has caused breakdown of bioligical filter resulting in ammonia/nitrite not being broken down sufficiently quickly. This could be a dead fish, over-feeding, too many fish in too small a tank, inadequate filtration.
Either way, for now, do whatever water changes necessary to get your ammonia and nitrite down as stated above. If you have some Prime water conditioner this will help ease the effect of the cycle. You can do 50% changes back to back no problem if necessary. It may be necessary to do twice daily changes.
Hope this helps & good luck