When speakers of a language coin words for one, two, three, four, etc., for the first time, where do they come up with the forms? Are there any common methods used across language families?
Pirahã has words for "few" and "many". Numerous other languages have only "one" and "many", possibly adding "two", especially among isolated hunter-gatherer tribes. If they do express numbers higher than that, it's by counting on their fingers in front of someone else. (See chapters 1 and 2 of The Number Concept, written by Levi Leonhard Conant in 1896.) But once people invent agriculture and trade, languages tend to come to have some system for counting and expressing, say, the number of animals in a flock or the number of days' travel to some other village.
If you can get past the use of "savage" and "rude" to refer to hunter-gatherers and "Aryan" for Indo-European, Conant continues to describe a common strategy for "five" through "ten". The word five is often some variant on "having finished one hand"; this is true of PIE as well where *pénkʷe (five) is related to "finger". Ten can be "having finished both hands" or (in the case of shod cultures) "one man", and six through nine "one more [than five]" through "four more"; nine is just as often "one less [than ten]". Barefoot cultures often adopt base 20 ("one man") with sub-base 5.
Some languages borrow numbers when their speakers borrow other cultural concepts. For example, most European languages borrowed "zero" from Arabic, and Swahili appears to have borrowed six through ten from the same language. Proponents of the Nostratic hypothesis will cite similarity between "six" and "seven" in IE and Semitic as evidence of common descent, if those words weren't also borrowed.
Conant lamented that the names of one through four appeared opaque in the vast majority of languages studied. Have the past 120 years produced any more clarity on trends in number word etymology among several language families? I tried Google
basic numbers etymology but most results appeared irrelevant, most simply tracing English back to PIE or reiterating that zero was borrowed from Arabic.