'Zero point one per cent.' Most common. 'Nought by one per cent.' Not uncommon, in the UK at least. If the number in front of the decimal is a zero, you can also just say 'point one per cent.' You can only really say 3.82% one way: three point eight two per cent. 0.24% would be 'zero point two four per cent','nought point two four per cent' or 'point two four per cent.' I've heard non-native speakers say things like 'zero point twenty four percent' but native speakers don't read decimals like that.

Paul and Dan have good answers, but personally, in rapid conversation, I would just say "point one percent" (and I have science degrees!)

I'm a U.S. native speaker. I personally would read this as "oh point one percent." I would read the others as "oh point twenty-four percent" and "three point eighty-two percent." In my science classes, I was taught always to put a zero in front of the decimal point. The reason is that the zero makes it easier to see that the decimal point is there and prevents errors. I carry this over into speech. I would always read the zero (as "oh") if it is printed, and I might well say it even if it is not printed. If, for example, I am trying to communicate over the phone to someone who was trying to transcribe what I was saying, then I'd read them character by character, reading 0 as "zero," thus "zero point one percent," "zero point two four percent." 0.1% is a special case. Depending on the context and how precise I think the value is, I might possibly read this as "a tenth of a percent." In a financial context, I might read it as "ten basis points!"

0.1% nought / zero point one per cent 0.24% zero point twenty-four percent 3.82%: three point eight two per cent.