Bob D. said:
"or even "free" as an apprentice)"
Disagree. NEVER place the value of your work at zero, even as a rank beginner/helper.
If you do you look worthless to whoever might hire you and to yourself you're saying you are worthless.
It's more about attitude than income, but it has an influence on your production and performance.
You work, you get paid. But you need to earn what you're paid. No free lunches and no free rides.
Over here it is common to pay for private schooling.
In that sense, working "free" is not really free here. It is about agreeing that one will "pay" a master to transfer the knowledge to one in exchange for his work/time instead of cash. This type of an arrangement is actually as old as people are social and existed before money was invented.
This can be a good deal for both sides in scenarios where the "attention" required to be given to a novice is making it a wash as if he was not there the master can do the work himself, thus not giving a master a rational reason to accept an apprentice.
In such a scenario is common that the apprentice is given above-his-skill tasks and the master is expected to invest his time to allow him to learn and complete the tasks.
Not everyone can afford that. One needs to live from something so usually this is done partially - the pay is agreed as subsistence-level only analogous to a mutual understanding only part of the work will pay for the schooling while rest will be paid for in cash.
But there is nothing bad in such an arrangement. Actually, it gives the apprentice a stronger position. If all work is taken as a compensation, it is harder to impossible for a master to abuse this unlike when just lower pay is agreed. And it is still advantageous economically as you avoid running your "tuition" through the taxes system which would take away half of it before it would reach the master ...
ADD:
Working for "free" to learn may not be legal in many jurisdictions so YMMV as the state may insist on having "its cut".
But I know of a couple such arrangements, were they legal or not I do not know, when friends who were total novices agreed for such to get their feet wet. Usually over a fixed time of a couple months and then either stayed as paid or moved on to seek a paid job/get a business etc. Was not in carpentry, but the concept of apprentice/master is not trade-specific in my view.