What is my nakṣatra and pada, and how do I find it?

your nakṣatra is the lunar mansion the Moon was in at birth; each is split into four padas (quarters).

The 360° zodiac is divided into 27 nakṣatras of 13°20′ each, from Aśvinī to Revatī. Your janma nakṣatra (birth star) is the one in which the Moon stood when you were born. Each nakṣatra has four padas of 3°20′, giving 108 padas in all — and each pada maps to a navāṁśa sign and a traditional starting syllable for a name.

The nakṣatra is used for many practical things: the starting daśā of your life, kundali matching (guṇa milan), choosing a name, and finding good days (tārā-bala). Families often remember a person's nakṣatra more readily than their lagna.

To find it you need your date, time and place of birth; the Moon moves through one nakṣatra in about a day, so the time matters, especially near a boundary. Enter your details in a birth-chart tool and it will show the nakṣatra and pada.

Source: Bṛhat Parāśara Horā Śāstra; Muhūrta Cintāmaṇi · 27 nakṣatras × 4 padas = 108

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