There are several schools of thought on this, and it is not a simple problem.
1) Fish only tank, no plants.
Fish food is the source of nitrogen, and there is no removal system other than water changes. There are associated things going on with the decomposing fish food, fish poop and the fish hormones, perhaps other things make water changes mandatory. The range of opinions seems to be that the NO3 should be kept under 20 ppm for optimum fish health. Some people insist that NO3 is not toxic, and can be really high. I do not know if NO3 itself is toxic, or perhaps it has to do with all the other things going on in the tank.
When I ran fish-only tanks I had them quite heavily stocked and had to do 50% weekly water changes to keep the NO3 under 20 ppm. If the NO3 started creeping up the fish became lethargic, and some diseases broke out. Mostly Columnaris.
2) Plants act to remove a LOT of toxins from the water. Maybe it is the plants themselves, or maybe it is a somewhat different group of microorganisms that thrive in a planted tank. I dunno. But a planted tank seems not to need as large water changes as a fish only tank.
3) If you are following the Estimative Index method of fertilizer then weekly 50% water changes are the way to start out. As you get to know your tank you can fine tune the fertilizer dosing and get by with smaller water changes.
4) No water changes will eventually deplete the carbonates in the tank. Some of the microorganisms use them as a source of carbon. When the KH drops, the pH drops. When the pH drops the microorganism population changes. This can make the tank toxic, but so slowly that the fish in the tank adapt, and survive. But new fish added are not so adapted, so they die. This is called Old Tank Syndrome and is basically a tank with not enough (frequency or volume) water changes.
I prefer to suggest you follow a schedule of perhaps weekly water changes. That way, you have a chance to get into the tank and correct things before they get worse. Clean the filter, vacuum the largest debris, trim the plants... a little this time, something else next time... so that the total maintenance is not done all at once, but spread out.
How much: As a place to start, use the NO3 test. Keep the NO3 under 20 ppm. If it has climbed to 40 ppm, then you will need to do 50% today, and perhaps another 50% tomorrow. If the NO3 is right at 20, then maybe need 50%, but maybe less is OK. Monitor it and see how fast it comes back.
If you have to add fertilizer to keep the NO3 stable for the plants, then try 25% weekly water changes. This will generate enough water to clean the filter.