For GA /tr, dr/, the tip of the tongue points slightly backward and forms a complete closure with the rear edge of the alveolar ridge, the rims forming a complete closure with the side teeth and gums. The front of the tongue is somewhat hollowed and contracted. Friction arises as a result of a slow release of the tongue tip. The lips are typically rounded.
GA /tr/ is usually realized as a voiceless post-alveolar affricate, [t̠ɹ̥], except when /s/ precedes in the same syllable.
The lenis counterpart /dr/ is initially devoiced after voicelessness: [d̥̠ɹ]. Although usually a post-alveolar affricate, GA /dr/ may also be realized as followed by a (voiced) homorganic approximant, especially in unaccented syllables.
Note that /t,d,n,l/ preceding GA /tr,dr/ will also be post-alveolar. Examples occur in card trick, hundred, oildrum.
A possible approach is to start with a slightly retracted [t]. Try to curl the tip slightly backward. Press the sides of the tongue firmly against the side teeth and gums, and release the closure by moving the tip of the tongue slowly backward along the hard palate. This should create the required friction. A similar approach, using a retracted [d] can be used for /dr/.
(The auditory and articulatory similarity between /tr/ and /t͡ʃ/, and, to a lesser extent, /dr/ and /d͡ʒ/ is quite considerable. It also appears from the spelling used by young English-speaking children, who will occasionally write ch(r) for /tr/, as in as chray, chrie, chribls, and chac for ashtray, try, troubles, track (Read 1975)).
Note that for /tr,dr/ the tip is curled back slightly and the front of the tongue is hollowed, while for /t͡ʃ,d͡ʒ/ the front of the tongue is raised in the direction of the hard palate. Heterosyllabic /tr,dr/- sequences, as in ratrace, handrail are not pronounced as affricates. In both words, /r/ is approximant. Exceptionally, wardrobe and bedroom frequently have an onset cluster /dr/, and are therefore pronounced with affricate [d̠ɹ].
Here are some words to practice /tr/ and /dr/.
trip, try, train [t̠ɹ̥]
drip, dry, drain [d̠ɹ]
intrude, retrace, untrue [t̠ɹ̥]
adroit, redress, undress [d̠ɹ]