The phonetic value of [h] is /h/. In English spelling, many phonetic units are digraphs, not monographs (unsurprising when you consider that English has ~40 phonemes but only 26 letters in its alphabet).
The core phonetic rules of English are actually quite simple:
* Map consonant digraphs to phonemes where appropriate (e.g., [ch] goes to /tʃ/, [ph] goes to /f/).
* Map remaining consonants to a single phoneme, although note that [c] and [g] will map to /k/ or /s/ and /g/ or /dʒ/ respectively depending on the following letter.
* Map vowel digraphs to their monophthongs or diphthongs (e.g., [ai] goes to /ei/).
* Map vowel monographs to their "short" or "long" form depending on the following letters (e.g., [bet] is /bɛt/ while [bete] is /bit/, same as [beat]). Basic rule is vowel-consonant-vowel gets the "long" form, otherwise you get the "short" form. Doubling a consonant forces the "short" form without implying a doubled (geminate) consonant in pronunciation.
Those rules predict a large fraction of English pronunciation. You can get better by adding in rules on schwa reduction (unstressed vowels become /ə/) or rules to reflect the systematic sound changes of the past few centuries (e.g., how [-tion] becomes /ʃun/). There are still irregularities beyond that ("English" isn't justifiable by any spelling rules), and then you have the frustrating tendency of English to insist on using foreign spellings and foreign pronunciations of foreign words (e.g., "coup" is French and should be pronounced as in French and "onomatopoeia" is Greek and should be pronounced as in Greek).