How is the γ in verbs like γιγνώσκω and γίνομαι pronounced in ancient Greek? Is it pronounced like g in get or like g in gem?
The letter gamma was pronounced like the g in get in Ancient Greek, a voiced velar stop. But before another gamma, before kappa, chi, or xi, the gamma was pronounced like ng, as in boring. It's also pronounced like ng before at least some cases of nu or mu (possibly all).
More information, including the pronunciation in New Greek, can be found on Wikipaedia: https://en.wikipedia.org/wiki/Gamma
In modern Greek it is pronounced exactly like y in yet.