In English, constituent question words are often called wh-words: what, when, where, which, why, whether. All these are spelled with a w and pronounced with a w (the h is pronounced in some dialects and not others). This is not coincidence.

The primary interrogative particle in Proto-Indo-European is *kʷ-, which is why so many constituent question words you might be familiar with in Romance languages like French and Spanish begin with qu-: qué, qui, quand, etc (though in Spanish and French examples, the u is no longer pronounced, they just start with a k sound). Also English words in the Latinate register related to questions, like question, query, inquisitive. ^[1]

Just apply Grimm's Law which changes PIE voiceless stops into voiceless fricatives in Germanic (among other things), and you get the Germanic forms with *hw-! (Later spelled wh- in Middle and Modern English.)

But then, we get who (spelled with a w-, but not pronounced), and how (no w- at beginning, spelled or pronounced). Note, these are the only ones spelled with an o. This is also not a coincidence!

We'll walk through the pronunciation and spelling of who and how one step at a time. (Note for pedants like me, I'll be intentionally skipping over some mostly irrelevant complications). what is included for comparison

Step 1

Proto-Indo-European. "How" is not yet a word, but it will be derived more or less from the singular instrumental form, *kʷónoh₁. "What" (*kʷód) is really just the inanimate/neuter gender of "who" (*kʷós).

Step 1: Proto-Indo-European
• "who": *kʷós
• "how": (*kʷónoh₁)
• "what": *kʷód

Step 2

Grimm's Law changes kʷ to hw. "how" is innovated from the Germanic instrumental case. Various other sound changes.

Step 2: Proto-Germanic
• "who": *hwaz
• "how": *hwō
• "what": *hwat

Step 3

Old English sound changes from Proto-Germanic.

Normally word final -az would be dropped entirely, but in *hwaz, with only one syllable, you can't drop it. Instead only the -z is dropped, and the a gets lengthened to aː to compensate.

In *hwoː, there is a vowel shift and the oː rasises to uː. But wait! /w/ and /u/ are only barely different sounds from each other ^[2]. So instead of Old English hwu, the w gets absorbed into the u that immediately follows it, and becomes just hu. There's no u in hwaː, so nothing happens to the w there.

Step 3: Early Old English
• "who": *hwaː
• "how": *huː
• "what": *hwæt

Step 4

Then English becomes a written language. At this point someone does the best they can to represent the sounds of Old English in a foreign (Latin) alphabet, and they did reasonably well. But then the sound changes just keep happening, and spelling sometimes changes with it, but usually doesn't, eventually creating a spelling system representing a mish-mash of various historical pronunciations.

Step 4: Mid Old English
• "who": hwaː, hwā
• "how": huː, hū
• "what": hwæt, hwæt

Notably, since this happens after the w is lost from huː ("how") in step 3, there is no reason to write it with a w.

Step 5

Sometime in the Old English phase, the sound written as hw changes from being h followed by w to a single sound merging the properties of h and w, represented in phonology as ʍ.

Step 5: Late Old English
• "who": ʍaː, hwā
• "how": huː, hū
• "what": ʍæt, hwæt

Step 6

In Middle English, "who" undergoes an irregular sound change turning aː into ɔː, and then a regular sound change turning ɔː into oː. The spelling is updated to reflect the change.

In all words, the spelling of ʍ change from hw to wh (both now equally valid, since the "w-ness" and "h-ness" are now overlapping instead of sequential).

Step 6: Middle English
• "who": ʍoː, who
• "how": huː, hu
• "what": ʍat, what

Step 7

The Great Vowel Shift happens, which totally screws English speakers for understanding vowels, because all the long vowels change pronunciation but mostly keep their spelling, but the short vowels don't change, and now what used to be closely linked short/long pairs are pronounced very differently, but still spelled as if they're related. Anyway, back to the topic at hand. Long oː shifts to long uː (compare, cool, good) and long uː shifts to the dipthong au. The short a in "what" is unchanged.

huː ("how") becomes pronounced hau, and hwoː ("who") should be pronounced *ʍuː. But wait, remember back in Step 2, when w couldn't exist next to u? The same thing happens here, and the uː absorbs the "w-ness" out of the ʍ, but leaves the "h-ness" behind. Instead of *ʍuː, hwo becomes huː.

Spelling changes update the spelling of words with ū/uu -> ow (au), but not words with ō/oo -> u, giving written forms who and how.

Step 7: Modern English
• "who": ʍuː, who
• "how": haʊː, how
• "what": ʍɒt, what

So in both "how" and "who", the pronunciation of the w is absorbed by the nearby u sound. But in the case of "how", the absorption happens before written English, so the w is neither pronounced nor spelled; but in the case of "who", it happens after written English, so the w is spelled but not pronounced.

Summary

		"who"		"how"		"what"
		pronunciation	spelling	pronunciation	spelling	pronunciation	spelling
Step 1	Proto-Indo-European	/*kʷós/	—	/*kʷónoh₁/	—	/*kʷód/	—
Step 2	Proto-Germanic	/*hwaz/	—	/*hwoː/	—	/*hwat/	—
Step 3	Early Old English	/*hwaː/	—	/*huː/	—	/*hwæt/	—
Step 4	Mid Old English	/hwaː/	hwā	/huː/	hū	/hwæt/	hwæt
Step 5	Late Old English	/ʍaː/	hwā	/huː/	hū	/ʍæt/	hwæt
Step 6	Middle English	/ʍoː/	who	/huː/	hu	/ʍat/	what
Step 7	Modern English	/huː/	who	/haʊ/	how	/ʍɒt/	what

Bonus fact

All of wh- words I mentioned at the beginning except when, can be derived from who by fairly simple morphology in Proto-Indo-European or Proto-Germanic or both:

• what is just the neuter/inanimate form of who.
• whom is just who in the dative case.
• how and why are from two different dialectic forms of the instrumental case ("by means of what").
• where is formed from who with the *-r Germanic suffix for location adverbs ("what place").
• whether is who with the contrastive suffix *-teros, effectively "who/what of those two"", and is related to, for example, English either and Latin alter: "the other one (of those two)"^[3].
• which is from who-like. That's more visible in the Scots form: "whilk". Compare also "such" from so-like.

Footnotes

1. ^

   This also why, to give a few examples, there are all those Greek and Welsh question words that start with p, and all those Irish, Hindi, and Russian question words that start with k, those being two common reflexes of Indo-European *kʷ.

2. ^

   This similarity between u and w is why the letters for these sounds are the same or similar in the Latin, Arabic, Hebrew, among alphabets. (And also v in many cases due a typologically common sound change w into v; Latin and Hebrew have that change for example.)

3. ^

   *-eteros *hwaþeraz ("whether") is originally "who/what of two" specifically. "who/what of many" is *hwarjaz. But only Gothic attests the distinction in 𐍈𐌰𐌸𐌰𐍂 ƕaþar vs 𐍈𐌰𐍂𐌾𐌹𐍃 ƕarjis. In North Germanic, sound changes merged *hwarjaz with *hwaz ("who"), and in West Germanic sound changes merged *hwarjaz to *hwar ("where").