The Rebbe's guidance on learning Torah by heart and on strengthening one's memory:
Learn by heart. Everyone, even businesspeople, should take part in learning Mishnayos by heart (IK 063, 078, 079). Completing and reviewing all six orders of Mishnah, especially by heart, has great spiritual value (IK 1982). What to memorize: Tanya and chassidic maamarim — not letters (IK 2794). A yeshiva student can memorize in his own free time without taking from the yeshiva schedule (IK 1992), and a bar mitzvah boy should learn portions of Tehillim, Mishnayos and Tanya by heart (IK 2788). One should strive to know both the Written and the Oral Torah by heart, though reciting written texts by heart as a set practice has its own halachic considerations (IK 5750, 9048).
Why it matters. Words learned by heart let you use every spare moment for Torah, even at work or when away from books (IK 2768, 6590, 8019). They fill the mind so there is no room for distracting or troubling thoughts (IK 2441, 2914).
Strengthening memory — natural means. Learn what you enjoy, switch subjects when tired, and don't strain the mind (IK 2552, 2884, 4389). Learn aloud and in a lively way, ideally with a study partner, and review what you learned (IK 5070, 6046, 8369). Renewed enthusiasm for learning brings improvement in memory (IK 2874).
Strengthening memory — spiritual means. Give tzedakah before prayer, check one's tefillin and mezuzos, review Mishnayos by heart, and keep to modest conduct (IK 4439, 6046, 6468). Immersion in a mikveh as instituted by Ezra and learning from a text also help (IK 3545, 6109).
See also: Torah study – Motivation, diligence and study partners; Prayer – Concentration and distracting thoughts.