Unfortunately, there's only one good way to know, and your teacher isn't giving it to you!
All vowels in Classical Latin are either "long" or "short". Long vowels were quite literally pronounced for longer, and also with a slightly different quality: long i was pronounced roughly like in English "beat", while short i was more like English "bit". Most instructional books will mark the long vowels with a line above them (ā ē ī ō ū ȳ) and the short vowels with the absence of that line (a e i o u y).
This is a fairly important distinction, since it distinguishes e.g. "old woman" (ānus) from "anus" (anus), or "one circle" (circus) from "multiple circles" (circūs), or "here" (hīc) from "this" (hic), or "mouth" (ōs) from "bone" (os), and so on. It's also crucial for poetic meter, and for getting the accent right. If your instructor hasn't mentioned it, I'd suggest bringing it up, and/or reading a bit about it on your own.
In this particular case, liber means "book", while līber means "free". You can also tell them apart in other cases, because "book" uses the stem libr-, while "free" uses the stem līber-: for example, "of the book" is librī, while "of the free person" is līberī.
Telling the difference between "free" and "children" is harder; the word for "children" comes from "free", so they look exactly the same. But "children" is only ever used in the masculine plural, so it always looks different from "books": "books" are librī, while "children" or "free men" are līberī. And if you're ever in doubt, that form almost always means "children"; if it's meant to be "free men", the context will make it clear.