How to pronounce the letter γ?
g as in "get",
but y as in "yet" before iota and epsilon.
n as in "sing" before gamma, kappa, xi, and chi.
(For clarification, the final sentence is referring to the "hanging n" sound in words such as ring, making, etc.
Here is some information on that sound if you need it: http://teflpedia.com/IPA_phoneme_/%C5%8B/)
A not bad YT video with the sound of γ is this: https://www.youtube.com/watch?v=0bsj_7vM1Dg
BUT, wait: γ can combined with some consonants, as it is "γκ". In this case there is a major difference:
1) 1.1.)These ones together are pronounced as a (non-nasal) g, as in the word "go", for the words which start from g and this g is pronounced "g" in the language of their origin i.e. γκάιντα=a oriental musical instrument, a word of Turkish (most likely, I don't know) origin.
1.2) "ng" (nasal g) like it "ng" in the word "English" for the Greek origin words, as i.e. in the word: ανάγκη=need. This is most usual case.
The problem is that the new learners do not know which words are of foreign origin. Well, you will get used to these words by the time, listening the pronunciation carefully. After all many Greeks make the same mistake, that is, to pronounce "γκ" as non-nasal g in all cases, a usual mistake that the linguists are getting upset.
Watch Prof. Babiniotis here, for the nasals: https://www.youtube.com/watch?v=esBeh4YYnio, in Greek (unfortunately). Prof. Babiniotis has written the most extent dictionary of Modern Greek, btw, and he is the most eminent living Modern Greek linguist.
-Notice (for those who had learned Αncient Greek at school) that they used to pronounce γ as g in all cases. But it is different in Modern Greek, actually it is a controversial point, which was the Ancient Greek pronunciation, the European and American learners prefer the Erasmean one, the Modern Greeks the Modern Greek one. But we don't learn Ancient Greek here, so it is out of question.
2) Combined with another γ, that is "γγ". it is pronounced always as nasal ng, as Ι don't know any foreign Greek word starting from γγ.
3) IN ALL other cases of combinations of γ with consonants it is γ, as in the first video, a special sound that is very similar with "y" in the word "yet". As in the word άγνωστος=αyνωστος=unknown.
Yes, I am trying to help the Greek learners. I love languages. And specially their structure and the comparative etymology. Greek is a basis to find key words and roots in many others, similar. And of course I cannot learn a language as a little child. The mental mechanism is different. But it is another discussion.
Even the English speaking speak Greek but some do not know. Example: What is the meaning of "economy" for an English speaking. Nothing. But it comes from Greek and it is composed by two words: οίκος=house, in Ancient Greek, and the Ancient verb "νέμω"=share, that is, "sharing the goods of the house". So it makes sense :) So saying οικονομία=economy is something that everybody can understand. Just as simple example how Greek can help to understand your own language.