Origins
The word 'how' is the manner interrogative in English, asking about method, means, degree, and quality. It descends from Old English 'hū' (how, in what way, by what means), from Proto-Germanic *hwō, from PIE *kʷō, an instrumental or adverbial formation on the interrogative stem *kʷó-.
The most immediately notable feature of 'how' is its spelling. Unlike 'what,' 'who,' 'when,' 'where,' 'which,' and 'why,' the word 'how' does not begin with the 'wh-' cluster that marks English interrogatives. This is not because 'how' has a different origin — it descends from exactly the same PIE interrogative stem as all the other 'wh-' words. The difference is phonological: Old English 'hū' descends from Proto-Germanic *hwō, where the /w/ element was absorbed by the following rounded back vowel /oː/. In the other interrogatives, the /w/ preceded front vowels or unrounded vowels and survived. The result is that 'how' is etymologically a 'wh-' word that lost its visual membership in the family through a regular sound change.
The PIE instrumental *kʷō asked 'by what means?' — a question about the instrument or method of action. Latin 'quō' (to where, by which way, to what purpose) is the direct cognate, showing how the instrumental sense ('by what means') and the directional sense ('to what place') overlap. German 'wie' (how) descends from the same Proto-Germanic form with different vowel development. Dutch 'hoe' (how) is the closest formal match to the English word.
Old English Period
Within English, 'how' functions as a degree word as well as a manner word: 'how tall is he?' asks about degree, not method. This degree use is ancient — Old English 'hū' already served both functions. The combination 'how come' (why, for what reason) is an American English innovation from the mid-nineteenth century, likely a shortened form of 'how comes it that...?' It has effectively created an additional 'why' word in informal English, blurring the boundary between manner and cause.
The compounds of 'how' are less numerous than those of 'where' or 'what' but include some important forms: 'however' (in whatever way, nevertheless), 'somehow' (by some means), 'anyhow' (in any case), and the archaic 'howbeit' (nevertheless — how + be + it). The greeting 'how do you do?' — now a fixed formula with no interrogative force — preserves 'how' in its original manner sense: 'in what way do you fare?'
Cross-linguistically, manner interrogatives are often derived from the same stem as other question words, but the derivational strategy varies. Greek used 'pōs' (how), from a different formation on the interrogative stem. Sanskrit used 'kathám' (how), with a different suffix. The consistency of the derivational source — the interrogative stem — with the diversity of the specific formations illustrates how PIE daughter languages independently elaborated a shared grammatical inheritance.