"How do people learn to land an aircraft properly when they have to pay for every landing?"
A far number of flying schools get free landing fees at there home base - although one could argue that this cost is paid and part of the shools rent.
I pay an annual fee at a couple of flying schools (about 100 quid for each) and as part of these terms I get unlimited T&G, Landing fees at those airfields.
This works pretty well but it doesn't give me access to night flying or instrument approaches which I still have to pay for.
Because of this I no longer teach night flying as its simply not cost effective. I also use AM radio stations to practice NDB procedures again in an effort to keep cost done.