It really depends almost exclusively on the sound of the letter following. If there's an "ε" or "ι" sound following, it sounds like the German "j" in the word "jeder" and like the "yi" in "yin", respectively. If it is followed by an "ο", "ω", or "α", it sounds like "go" or "ga" in Spanish when it's in the middle or end of a word, like "fuego" and "delgado", respectively.
ΓΚ is the English G in go
Γ is Y in yes * **BEFORE an
ε-sound (αι, ε) or an
ι-sound (ει, η, ι, οι, υ)
OTHERWISE a French R or gargle g in your throat
Futhermore Greeks transcribe foreign names so that they pronounce them exactly like the originals: Τζωρτζ Γκέρσουιν = George Gershwin, Γκράχαμ Γκρην = Graham Green, Γέιλ = Yale , Όσκαρ Γουάιλντ = Oscar Wilde
Audio: Why does she pronounce the ς in the γεγονός like a sh instead of a s?. I am dependent on learning by hearing and training (learning a natural way) before I am able to understand grammar from books...so please, make the audio on the basic level right! The audio is what could make Duo Lingo different from all other language courses, the audio is the most important thing to be correct!
I can totally understand your confusion. As I posted above, the gamma is closer to the Spanish 'g' before certain vowels inside the word (not in the beginning of it) and before the 'r' (again inside the word). But the course is directed to speakers of English, and the closest equivalent is the 'w'.
You learn by mistake and repetition. Before starting a lesson you're able to see what words that lesson will teach. In advance you can search for the meaning or you can simply learn by your mistakes while taking the lesson. The ultimate prize that you win in Duolingo is learning. :-)