it sounds like you tank is already started to cycle, the green water is a bacterial bloom. cycling is just letting you tank build up benifical bacteria.
before you cycle a tank you should put in your gravle, filter, decoration and whatever so your bacteria have a place to colonize. then add water then add an ammonia source, like fish food or pure ammonia. the bacteria change the ammonia into nitrite, then to nitrate. once you have your nitrate you need to do a 90% water change to bring it down.
ammonia should be 0
nitite should be 0
nitrate should be under 20
so yes you do need a liquid test kit that messures ammonia, nitrite, and nitrate, (ph is good too) to track your tanks progress though the cycle
this process can take from a few weeks to a couple months. here is a link to more cycling info