Don't replace the filter, as this is the main area where bacteria grow. "cycling" is referring to the nitrogen cycle, where bacteria consume nitrItes and and ammonia and and end product is nitrAtes, where then it (ideally) would be consumed by plants, or would be removed with a water change.
First you should try getting a liquid kit, as strips are notorious for being inaccurate (and more expensive for that matter).
Walmart used to have this for around $15, but now it's 25$, but just to give you an idea
Walmart.com: Freshwater Master Test Kit: Fish
Thirdly, you want to keep ammonia and nitrItes under .5ppm, and nitrAtes under 40ppm. You'll have to do up to a few water changes a day to keep these levels, but your oscar will be better off.
Cleaning will involve removing up to 40% of the water, and vacuuming the uneaten food off the bottom.
Finally, if you live in the city (don't have a well) make sure you dechlorinate your water (either by outgassing or a dechlorinator), because this will kill off your beneficial bacteria.