Press your lips together. Air flows through your nose. Vocal cords vibrate.

Americans pronounce maritime as MAIR-uh-tahym (/ˈmɛrəˌɾaɪm/). Stress falls on the first syllable — keep everything else short and quick. You'll hear it in sentences like "The maritime dispute has been referred to international courts".
Record yourself saying "maritime" and play it back. The mic stays on your device — nothing's uploaded.
3 syllables, 6 sounds. Tap a syllable to jump to its row, then explore each sound's mouth shape and how it's made.
Quickly bounce the front of your tongue against the roof of your mouth. Don't stop the airflow — just a quick tap.

Start with your jaw open wide and your tongue resting low and flat. Glide the front of your tongue up toward the roof of your mouth as your jaw closes halfway.
Press your lips together. Air flows through your nose. Vocal cords vibrate.

The textbook way isn't wrong — it's just not how anyone actually says it.
Stress falls on the first syllable, not the others. Stretch MAIR — keep everything else short and quick.
Don't pronounce the first syllable too fully. The unstressed syllable reduces to a schwa — the lazy "uh" sound — in casual speech.
Americans use a relaxed retroflex R — the tongue curls back rather than rolling. The R is one continuous sound with the vowel before it, not two separate sounds.