We don't. The original pronunciation was lost, as the speaking of God's name is (and was historically) widely disapproved of by the Jews. Here is an excerpt from The Jewish Religion: A Companion reprinted at My Jewish Learning, discussing the Tetragrammaton and talking about this very subject in the first few paragraphs.

I am going to expand upon my previous brief reply comment. Basically, 'Yahweh' or 'Yahveh' are our "best scholarly reconstruction for how YHWH was pronounced.

The first fact we need to deal with is that Hebrew was previously written without vowels. Vowels in Hebrew are indicated by 'vowel pointing' (Niqqud), the dots and lines typically written above and below the consonants. Vowel pointing was introduced by the Tiberian Masoretes in the early middle ages, and aimed to preserve pronunciation practices. It is typically not used in modern Hebrew, and if you know Hebrew you can read it, generally, without vowels because you know what vowels 'should' be there. They are very helpful though when consonants by themselves are ambiguous.

Prior to the introduction of vowel pointing, some letters in the consonantal text sometimes function to indicate vowels. This includes he, vav, yod, alef.

By the time the Masoretes were introducing vowel points, there were some words in the consonantal text that were often 'read' aloud differently to how they were written. Their respect for the integrity of the text mean they kept the consonantal text in tact, but they would often indicate how such words would be read by writing the vowels of the 'read aloud' word along with the consonants of the word written. These tend to be called 'qere' (read) and 'ketib' (written).

Over some time, and it's difficult to pinpoint when, Jews stopped pronouncing the divine name YHWH, ostensibly to safeguard against violating the command against taking YHWH's name in vain. This practice lead to the standard substitution of 'Lord' or 'my Lord' (Hebrew Adonai) for YHWH. The Septuagint versions tend to substitute 'Lord' (Greek Kurios) for YHWH, though there is some debate that early LXX texts retained YHWH in some manuscripts.

Some other Greek texts preserve renders of YHWH into Greek as 'Iao' or something similar, as is found among early Christian writers.

So, when we come to the text of YHWH, it is typically written with vowel points that indicate reading 'Adonai', or in some cases 'Elohim' ("God"; it is read this way when the text has Adonai YHWH, in order to avoid reading Adonai-Adonai). Using the vowels of Adonai with the consonants of YHWH gives a reading of Yahovah, which is where "Jehovah" originates from. This is almost certainly incorrect.

The suggestion of 'Yahweh' lies with Wilhelm Gesenius, whose argument rests primarily upon the compnent YHW/YH in 'theophoric' names (names that embed a component of a God's name), as well as the traces of pronunciation preserved in early Greek translations, such as Theodoret's preservation of the Samaritan pronunciation 'Iave'. His material can be read in Samuel Tregelles' translation of Gesenius' Hebrew-Chaldee lexicon of the Old Testament.

It will be helpful to note that when transliterating across languages, depending upon the letters available and the sounds they represent, i/j/y and w/v/b can be somewhat interchangeable.

In short, we don't know for sure. Indeed, certainly is probably unreachable, but 'Yahweh' remains our best conclusion at present.

Follow up:

Where does the idea come from that YHWH should be pronounced with a inward breath then an outward breath?

There are rare cases where it was not pronounced Yahweh. Letters from the jewish community of Elephantine in egypt under persian rule (V - IV century BC) mention a divergent pronounciation, something more like "Yahou".

I am not a Biblical scholar nor a Hebrew speaker, so forgive me if I may be mangling this. But I have heard a theory that YHWH may possibly borrow from the name of a Canaanite god known as YHW.

Briefly, the ancient Egyptians had a term "Shasu" for various pastoral nomads in the Levant. They were grouped according to where in the Levant they lived, for example "Shasu of Rbn", "Shasu of Sm't", etc. One of these groups were the "Shasu of Yhw". These names are listed on one of the columns at the temple of Soleb, dating about 1360 BC. I understand they were also repeated at the temple of Ramesses at Amrah. The inscription marks the victory of Ramesses II over the Shasu in the southern Canaan.

Apparently, it was common back in the day that the town and the god were synonymous, meaning that YWH may refer both to the town ("the Shasu who lived in YHW") and the local god of the town named YHW.

Now the Bible refers to these Shasu as the Midianites - the inhabitants of southern Canaan, what is today Jordan and northwestern Saudi Arabia. According to the Bible, Moses fled to Midian after killing the Egyptian overseer, and spent 40 years there as a shepherd, tending flocks for a Midianite priest named Hobab or Jethro. He married Jethro’s daughter, Zipporah. The incident of the burning bush, where Moses first encountered god, also happened in Midian.

After Moses went off to free his people from Pharaoh, he returned to Midian to where he had encountered the burning bush, and spent 40 days and 40 nights on the same mountain, after which god gave him the 10 commandments. Around the same time, Jethro and his daughter Zipporah joined him, and Jethro was among his advisors who asked him to delegate some of his work, hence his appointment of Judges as mentioned in the old testament.

So the theory is that if Moses lived among the Midianites, he was probably well aware of their gods, including YHW. It is interesting that Moses spent 40 years working for a Midianite priest, and married his daughter. And that the same priest later joined Moses after the exodus, and helped him establish some of the early rules of administration of the Mosaic religion.

The reason why this may be relevant is because the Egyptian inscriptions about the Shasu are in hieroglyphics, where YHW is read as “Yahoo”. I wonder if this was perhaps the original pronunciation of the name.

Of course, I don't know much about the historicity of Moses, and this theory relies heavily on the historicity of the Bible. I don't know how accurate it may be. Perhaps some historians could comment.

Am I the only Jewish person that is feeling crazy for not knowing or ever hearing the name Yahweh before? It's always just been G-d or Adonai my entire life...never EVER heard Yahweh mentioned in the years of Sunday school, Bar Mitzvah classes, Confirmation, or any sermons until just last week when discussing amongst friends.

Is this a name that Christians typically use?