The primary duties of a brAhmin are adhyayana (studying) and adhyapakatva (teaching). Some enlightened people like Vasistha also worked as purOhita of a king.
The following is from Bala Kanda of Ramayana.
स्वकर्मनिरता नित्यं ब्राह्मणा विजितेन्द्रियाः | दानाध्यानशीलाश्च
संयताश्च प्रतिग्रहे || १-६-१३
The sense-controlled scholarly Vedic Brahmans are always engaged in
their rituals, and they donate the education of Vedas to their
students, as well practice their own, and while receiving donations
they are principle-minded.
The donations received by Vedic scholars are not alms to beggars or
charities to the destitute. The Vedic scholars do not receive them
from anybody or everybody. There are set rules to accept such
donations like cows, gold coins, villages, temples etc., from a
befitting hand. Otherwise, the recipient is destined to go to Hell for
having received greedily. Thus, if ever somebody wants to donate to
such a scholar he should first notify his bona fides, which are
verifiable by the recipient. Another kind of donation is referred here
as daana-aadhyaana, meaning that these scholars while receiving
donations from a righteous source, they also have to donate something
to others. It is the education in Veda, which they have to impart to
their students free of any charge and that too, to the befitting
students only. Thus, the words, daana and pratigrahaNa mean all these
rules to accept a donation or to accord it.
Another source is Sutta Nipāta of Buddhism (P.101), in which Gautama, the Buddha praises the high valued life of a brahmin of earlier age.
Brahmins then no cattle had, no gold, no grain they hoarded up, their
grain, their wealth was Vedic lore— this the treasure they guarded
well.
For them, whatever food prepared was by the doorway placed from faith
prepared for those who sought, for (donors) thought it should be
given.
Then in various states and provinces rich in colourful cloths
well-dyed with furniture and dwellings too with these to brahmins they
paid respect.
Unbeaten were brahmins and inviolate— guarded by Dharma-goodness then,
none hindered or obstructed them when they arrived at household doors.
Until the age of eight-and-forty they practised celibate student life—
the brahmins of those ancient times fared seeking knowledge and
conduct good.
