Shree Krishna in the Bhagavad-Gita has listed out the qualities of true Vaishnavas in the twelfth chapter:
He who has no hatred towards anybody, who is friendly and compassionate, who is free from the sense of possession and egotism, who looks upon all pain and pleasure the same as and who is enduring; He who is content, who ever meditates and is self-restrained and who is firm in his convictions, who has the mind and reason dedicated to Me-he is very dear to me. He from whom the world has no cause to be frightened, who is not frightened by the world, who is free from joy and impatience, fear and repulsion-he is very dear to Me. He who is free from desires, who is pure, expert, indifferent from agony, who has renounced every undertaking-he is very dear to Me. He who rejoices not, nor hates, nor grieves, nor desires, who renounces good and evil, who is full of devotion to Me-dear to Me is such a devotee. He who is same to foe and friend, honour and dishonour, who is alike to both cold and heat, pleasure and pain, and who is free from all attachments; He who regards alike both blame and praise, who is silent and content with any lot, who has no home, who is firm of mind, and who is devoted to Me-dear to Me is such a man. But those devotees who follow this nectar of virtuous duty as taught above, who are full of faith and who regard Me as supreme-they are exceedingly dear to Me. (Bhagavad-Gita, Chapter 12, Verses 13-20)
Narsinh Mehta, a Vaishnava saint in the fifteenth century has listed the qualities of a true Vaishnava in his famous poem "Vaishnava Jana To"
vaiṣṇava jana to tene kahiye
je pīḍa parāyī jāṇe re,
para duḥkhe upakāra kare to ye
mana abhimāna na āṇe re
sakaḷa loka māṁ sahune vande,
nindā na kare kenī re,
vāca kācha mana nischala raakhe,
dhana dhana jananī tenī re
sama-dṛṣṭi ne tṛṣṇā tyāgī,
para-strī jene māta re,
jihvā thakī asatya na bole,
para-dhana nava jhāle hātha re
moha māyā vyāpe nahi jene,
dhruda-vairāgya jenā manamāṁ re,
rāma-nāma shu tāḷī lāgī,
sakaḷa tīratha tenā tanamāṁ re
vaṇa-lobhī ne kapaṭa-rahita che,
kāma krodha nivāryā re,
bhaṇe narasaiyo tenuṁ darasana karatāṁ,
kuḷa ekotera tāryā re
English Translation: Him we call a Vaishnava who realises the pain of others. Who helps those who are in misery, without letting pride enter his mind!
One who respects the entire world, who doesn't disparage anyone. Who keeps his speech, deeds and thoughts pure, blessed indeed is the mother of such a being!
One who sees all equally and relinquishes cravings, who reveres other women as his own mother. His tongue may tire, but never utter untruth, and his hands never touch others' wealth!
One who doesn't succumb to worldly attachments, who's mind is deeply rooted in staunch renunciation. He is immersed in chanting Sri Rama's praises and all holy pilgrimage sites are embodied within him!
One who is devoid of greed and deceit, and has forsaken lust and anger. Narsinh says, "I'll be grateful to meet such a soul, whose virtue liberates the entire lineage."