In English, some H words are heard; some are silent.
Go here for tongue twisters to help you get it straight.
In American English pronunciation:
MOST words that begin with H are heard (e.g., hard, have, happy);
A handful of words that begin with H are always silent (e.g., heir, hour, honor); and
A few words that begin with H are flexible, depending on the speaker's family or community practice of pronunciation (e.g., herbs, humble, humor).
When in doubt, make your H heard.