Push a stream of air from your throat through your open mouth. No tongue or lip contact.

Americans pronounce heartfelt as HART-fehlt (/ˈhɑrtˌfɛlt/). The L in "heartfelt" is a dark L — the back of the tongue rises toward the soft palate, adding a small "uh" quality before the L. This is called the Dark L vs Light L, and it's one of the defining features of casual American English. It comes out as HART·FEHLT. Stress falls on the first syllable — keep everything else short and quick. You'll hear it in sentences like "Please accept my heartfelt apology for being so thoughtless".
Record yourself saying "heartfelt" and play it back. The mic stays on your device — nothing's uploaded.
2 syllables, 7 sounds. Tap a syllable to jump to its row, then explore each sound's mouth shape and how it's made.
Push a stream of air from your throat through your open mouth. No tongue or lip contact.

Open wide for the 'ah' vowel. Lift the tongue back and up while flaring the lips for the 'r'.
Touch the tip or front edge of your tongue to the roof of your mouth just behind your teeth. Keep your jaw relaxed. Stop the air, then release with a puff.

Lift your bottom lip to touch the very bottom of your top front teeth. Blow air through this contact point without voicing.

Drop your jaw moderately. Touch the tongue tip behind the bottom front teeth and lift the mid-front part slightly toward the roof.

Keep the tongue tip down and pull the back of the tongue up toward the throat. The 'dark' sound comes from the back.

Touch the tip or front edge of your tongue to the roof of your mouth just behind your teeth. Keep your jaw relaxed. Stop the air, then release with a puff.

The textbook way isn't wrong — it's just not how anyone actually says it.
The L in "heartfelt" is a dark L — the back of the tongue rises toward the soft palate, adding a small "uh" quality before the L. Dark L adds a small schwa-like "uh" before the L. The back of the tongue lifts toward the soft palate.
In "heartfelt", the "t" is not released — the articulators get into position but hold without the burst of air. Air stops but there's no release burst — the articulators hold position.
Stress falls on the first syllable, not the others. Stretch HART — keep everything else short and quick.
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.