Chanting the holy names of Lord (or nama) Hare Krishna Hare Krishna | Krishna Krishna Hare Hare | Hare Rama Hare Rama | Rama Rama Hare Hare is done in two ways - Nama Japa and Nama Sankirtana.
Nama Japa
Nama Japa is a personal remembrance of Divine Lordships on japa-beads. It is a personal seva. It purifies the sadhaka's (devotee who chants) consciousness by destroying all anarthas(conditioning) from the heart and elevates him/her to the level of prema in a gradual process. For sincere and serious seekers, you can refer to the book Madhurya Kadambini by Srila Viswanath Cakravarti Thakura Prabhupada to learn more about the different stages of bhakti.
Nama Sankirtan
Nama Sankirtana is congregational singing and chanting of holy names of Lord. It is a group seva. It elevates the sadhaka gradually to the inner confidential pastimes of Lord, depending on his / her surrender and sincerity. In Kali Yuga, the entire scriptures culminate at Yuga-Dharma Harinam Sankirtana Yajna. Just by participating in more and more kirtan with full engagement, you will get the inner direction within your heart. Just keep remembering Srila Prabhupada, guru-shishya parampara and the Divine Couple during kirtan and things will be revealed gradually.
Aindra Prabhu says that nama japa is like nikunja seva and nama sankirtana is like rasa lila. He also adds that "dono chahiye" or both are important. For devotees who want to dive into this rasa, do read Aindra Prabhu's book The Heart of Transcendental Book Distribution by surrendering to the guru-shishya parampara. This book is highly recommended for devotees who are really serious about attaining vraja prema bhakti and going back to Godhead in this very one lifetime itself.
Devotees who are in Krishna Consciousness for more than 3-5 years and who have read the Bhagavad Gita, Bhagavatam and foundational books by Prabhupada must-read Aindra Prabhu's book to dive in the inner aspects of vraja-prema bhakti, which in fact is something Prabhupada has mentioned in all his books and lectures, but hidden it in a subtle manner so that sadhakasand aspiring seekers don't take it cheaply owing to lifetimes of conditioning (vikar), and with gradual vaidhi bhakti (rules-based bhakti) and mercy of Krishna Chaitanya Mahaprabhu, approach their bhajan sincerely with deeper understanding.
NOTE: This excerpt is a part of the article Why listening to kirtan of Srila Prabhupada, Aindra Prabhu and Rasika Vaishnavas (and surrendering to them) help attain Vrindavan Prema Rasa quicker?