As you see, the following are international phonetics in German for König and Leipzig:
[ˈkøːnɪç] [ˈlaɪptsɪç]
My question is how to pronounce the g, i.e., [ç] properly? Does it pronounce as close as ch in change (an English word), or sh in shoe (an English word), or h in hot (an English word)?
Any help would be appreciated.
If you are really asking about the closest ENGLISH equivalent of the German ich-Laut I would suggest that you duplicate the initial sound in the English word “human”. Phonologically speaking, the German /ç/ is the voiceless equivalent of voiced /j/, so it is very similar to the English /hj/,
No, it does not pronounce like change, shoe or hot or any other English word. The sound you need is not even similar to any sound that exists in English. Pronouncing this sound correctly is one of the hardest things to learn for an English native speaker. (I think it's even the hardest pronunciation task.)
Der König ist selig, wenn er in Leipzig ein wenig Honig isst.
The king is delighted when he eats a little bit of honey in Leipzig.
For words ending in -ig (König, selig, Leipzig, wenig, Honig, and a lot of others) there are four different pronunciations:
the "standard" pronunciation with [iç]
This pronunciation is what you mentioned in your question [ɪç]:, like in the German word »ich«.1
[deːɐ̯ ˈkøːnɪç ɪst ˈzeːlɪç vɛn eːɐ̯ ɪn ˈlaɪ̯pt͡sɪç aɪ̯n ˈveːnɪç ˈhoːnɪç ɪst]
This pronunciation is the dominant pronunciation north of (about) the line Karlsruhe - Stuttgart - Ingolstadt - Passau, with exceptions mentioned below.
The majority of German native speakers live in this area, and it's also the pronunciation that German speaking actors learn (Siebssche Bühnensprache) during their actors education, even when they live south of this line. Both facts are the reason why this is considered to be the standard pronunciation. This is also the pronunciation that learners of German as a foreign language should prefer (except they live in a German speaking area south of this line).
the real southern pronunciation with [ig]
South of the geographic line mentioned above, including whole Switzerland and Austria, people don't use [iç] for »-ich« at the end of a word. Instead they use [ig]:
[deːɐ̯ ˈkøːnɪg ɪst ˈseːlɪg vɛn eːɐ̯ ɪn ˈlaɪ̯pt͡sɪg aɪ̯n ˈveːnɪg ˈhoːnɪg ɪst]
I was born in Graz, lived there for 30 years, then 20 years in Vienna and now 60 km west of Vienna in St. Pölten, and in this region (the eastern part of Austria) you will hear almost only [ig]. But there is one strange exception: In the prominent Viennese workers dialect you will hear very often [iç]: »Selig« [ˈseːlɪg] becomes »sölich« [ˈsøːlɪç] in this dialect. But I don't speak this dialect, so I use [ig]. (In the same geographic reason [z] is used very rarely and is almost always replaced by [s].)
the theoretical southern pronunciation with [ik]
[deːɐ̯ ˈkøːnɪk ɪst ˈzeːlɪk vɛn eːɐ̯ ɪn ˈlaɪ̯pt͡sɪk aɪ̯n ˈveːnɪk ˈhoːnɪk ɪst]
There is an interesting phenomenon in the pronunciation of German: Final-obstruent devoicing (in German: Auslautverhärtung). This means, that voiced plosives (in German: weiche Konsonanten = soft consonants) (b, d, g) will be pronounced voiceless (in German: hart = hard) (p, t, k) if it's the last sound of a word. So, this phenomenon turns each and every [g]-sound that appears at the end of a word into a [k]-sound.
German native speakers do this, but most of them are not aware that they do it. They also do it when they learn foreign languages, that don't have final-obstruent devoicing (like English, French or Italian), and this is an important part of the typical German accent that many German native speakers have when they speak such a foreign language.
But this is only half of the truth. If this was fully true, then the pronunciation that I use (with [ig]) wouldn't exist. But it does. The reason is, that also the German final-obstruent devoicing is subject of a geographical pronunciation difference. Final-obstruent devoicing does not happen (or happens in a way less amount) in southern regions of the German speaking area, but I'm sorry, I don't know where exactly the borderline is in case of this phenomenon.
the Saxonian-Palatine pronunciation with [ɪʃ]
In the German states Saarland and Rhineland-Palatinate, but also in Saxony you will hear this:
[deːɐ̯ ˈkøːnɪʃ ɪst ˈzeːlɪʃ vɛn eːɐ̯ ɪn ˈlaɪ̯pt͡sɪʃ aɪ̯n ˈveːnɪʃ ˈhoːnɪʃ ɪst]
I never witnessed this pronunciation on my own, but this is what the Atlas der Alltagssprache claims. There you can also see a nice map for the pronunciation variations of »König«, »wenig« and »zwanzig«, across Germany, Switzerland and Austria. There you also can see, that some individual speakers in the north prefer the variant that I called here the »theoretical souther pronunciation«.
But note, that the makers of this map explicitly excluded the variation [ig] in their survey, so they did not take care of geographical variations of final-obstruent devoicing, and this is why you don't find the possibility »König« in this map.
1 Note, that there are two sounds for »ch« in German: ich = [ɪç] and ach = [ax]. Thats's why they are also called »ich-CH« ([ɪç t͡seːhaː]) and »ach-CH« ([ax t͡seːhaː]). It depends on the vowel before »ch«:
But this rule is only valid if the vowel (or diphthong) and »ch« belong to the same syllable. If a syllable begins with »ch« then it's always [ç]. This is always the case for the diminutive syllable »-chen«:
In my experience it's none of the above. The closest English sound is probably 'sh' as in "show", but the German 'g' in "-ig" is formed further back in the throat, though not as far back as the 'ch' in "Bach". In some regions it's pronounced differently though, more (but not exactly) like a 'k'. (Like most languages, there are regional differences in pronunciation.)
I'm still not sure why you're asking this type of question here though. Most online dictionaries have sound files so you can listen to a native speaker saying any German word that's likely to come up, and Google Translate has automated text reading so you can listen to full sentences if you want. (Somewhat robotic sounding but close enough for most purposes.) Plus there is no shortage of videos in German. We can't teach you how to speak like a native German; that takes practice listening and repeating. IPA and other written descriptions are only going to be approximations.
Of the three given options ich-CH is closest to English h, gh. The developments that lead to ch and other purportedly lenis phonemes are are fairly similar, eg.
In fact, the ch-sound was frequently spelled with a mere h. It does in most cases stem from *K. The onset in knife has disappeared completely, for example. However, /h/ is aspirated whereas /ç/ is a palatal fricative. These are not contrastive in German but phonetically conditioned allophones. The spelling of long vowels with h is a relic of contrastive lengthening when following consonants were lost.
For similar reasonz, ch is indeed similar to shoe /ʃ/ and chill /t͡ʃ/ but this is kind of secondary to the above. *sk affricated in German and English at least, cp. shirt, Schürze, but Norse gave us skirt. Whether that's the same development as *k > h, cp. Haut, hide, Latin cutis, is difficult to judge. Equivalently, /t/ has iotazised on occasion, eg. tune, choon /tjuːn/, /tʃuːn/. In effect, /s t/ are coronal, ie. produced with the tip of the tongue, whereas /k c/ require a palatal place of articulation, ie. with the dorsal tongue going towards the roof of the mouth. /ʃ/ can be both, though the allophonic place of articulation varies rather closer to the alveolar ridge instead of the hard palate. So, ignoring the coronal onset you are almost there, eg. /(t͡)ʃɪl/ becomes chillipepper may become /ʃiːli/ or rather Cayenpfeffer.
Now approximate a /sk/, affricate and move the tip of the tongue slightly forward and lax. Alternatively, you can think of it as a plosive /k c/ in reverse.
Except that it does not appear syllable initial.
/g/ is also relevant, cp. Micky, Michael, Miguel, Mihial. However, the voice distinction is contrastive, cp. Meier, Maior, mayor, major, Latin mega ~ maioris, older German michel, Sanskrit maha "big", hence also mighty, mächtig, in contrast to meager. The voice distinction has later been erroded, anyhow.
In result, the articulation of /ç/ varies widely, because the noisy, turbulent airflow is rather unspecific. Nevertheless it can be a distinctly audible marker.
König: The Uber-German stop /g/ may have come under the same lenition in low countries, perhaps due to Carolus M. Rex, Gothic cognates not evident. On the other hand, *kuningaz < *kunją ("clan, family", PIE *ǵn̥h₁-yo-m) modulo *-ingaz may be as explained as -ig / *-ja from *-yo-m, cp. [*Hyós] (https://en.wiktionary.org/wiki/Reconstruction:Proto-Indo-European/y%C3%B3s) "that", perhaps as elipses and metonymy, not unlike "the crown", or rather from *ju, cp. ius "the law".
Leipzig in contrast is from a Slavic placename, locally still called Leipz'sch, earlier ...
... "Lipsk", meaning "place of linden trees"; compare Lower Sorbian lipa, from Proto-Slavic *lìpa, from Proto-Balto-Slavic *léiˀpāˀ. Early spellings of the name in Latin include Libzi, Lipzk and the standard Lipsia. (https://en.wiktionary.org/wiki/Leipzig#German)
