The Rebbe's guidance on saying Tehillim — daily, in groups, and at special times:
Every day. Saying Tehillim every day carries tremendous merit; keep the custom and don't drop it even when busy with other study (IK 3095, 3832). Daily Tehillim brings blessing into the home (IK 2850). Tehillim has a spiritual power akin to Torah study (IK 186). Keep it up in every circumstance, even during army service (IK 6558), and say Tehillim on Shabbos and Yom Tov as well (IK 3618).
Your own chapter. On one's birthday, say one's own chapter of Tehillim (the chapter matching one's new year of age), give tzedakah and learn Chassidus (IK 1548, 2116, 3562, 9777). The Rebbe also encouraged saying the Rebbe's chapter (IK 658).
Tehillim together. Found and strengthen Tehillim societies and groups (IK 033, 053, 2513, 9285) and publicize them (IK 7768). Introduce Tehillim in shul, even on weekdays (IK 1008, 8770). On Shabbos Mevarchim, the whole book is said together before davening (IK 4436, 6002). The names of Tehillim societies and their members were mentioned in prayer on Hoshana Rabbah (IK 7770, 7771, 7792).
Specific chapters. Psalm 27 is said daily in Elul (IK 9965, 1163). For worry, learn and say Psalm 23 (IK 8757, 9571). The Rebbe recommended Psalm 71 for blessing in body and spirit (IK 667). For bedtime and night practices see IK 6069, 7366 and 8242; on Psalm 25 in Tachanun see IK 3117.
At times of need. Alongside the doctor's advice, saying Tehillim and giving tzedakah are powerful remedies for illness (IK 660, 1409) and support a healthy pregnancy and birth (IK 1176, 1315, 1626).
See also: Prayer – Praying for others and at the Ohel; Bitachon – Worry, fear and anxiety.