They didn't unless they were well off. Only 8% of houses had a computer in 1984. 15% by the end of the decade. C64 was $595 new, if you had one I doubt your family was poor.
I bought a TS1000 in 1981 or 82 for $99, and a C64 in probably spring 1983 for $299 at Circuit City. I was in 9th grade and used paper route money to get it (parents thought they were glorified Atari 2600's). Hehe, remember newspapers and paperboys?
I'm surprised only 8%. My memory of growing up in the UK in the early 80's was that ZX81'S and ZX Spectrums were super common. I bought my ZX81 in 1982 for £50 new which looks like it was maybe $80.
One of the reasons the Spectrum was so common was the low price. And of course using taps for games meant that most weren't paid for, but copied and shared around at school.
I grew up with the ZX Spectrum, like so many others, and it is what started me programming/developing/being interested in computers.
The UK actually had the highest level of computer ownership in the world at around that point.
You're probably looking at it from a biased point of view though. When I was growing up everyone had a Snes. Of course it was just all teenage boys that had one.
There seems to be a few C64's including breadbin and C64C models on eBay most days that I look. Granted some may need recapping or other work done, but there are plenty of others in working condition or only needing minimal repairs. I think you could get one for not much more than $US200 + plus shipping.