A few days back I noted this link about Nṛsiṃha caturdaśi vrata by jyotishi Shyamasundara Dāsa.

I’m just going to note a few things here from my edition of Hari-Bhakti-Vilāsa

atha niyamamantraḥ

श्रीनृसिंह महाभीम दयां कुरु ममोपरि|

अद्याहं तो विधास्यामि व्रतं निर्विघ्नता नय||

Translation: O Lord Nṛsimhadeva! O greatly powerful one, please display compassion toward me. To day, I will observe this vow of Yours and so kindly help me to complete it without any impediment.

śrīnṛsiṃha mahābhīma dayāṃ kuru mamopari|

adyāhaṃ to vidhāsyāmi vrataṃ nirvighnatā naya|| iti ||

The pūjā prescribed is a shodashopachara(16 upācāra) puja. Before Nṛsiṃha is worshipped,Prahlāda must be worshipped as well.

candanamantra

चन्दनं शीतलं दिव्यंचन्द्रकुङ्कुममिश्रितम्|

ददामि ते प्रतुष्ट्यर्थं नृसिंह परमेश्वर||

candanaṃ śītalaṃ divyaṃcandrakuṅkumamiśritam|

dadāmi te pratuṣṭyarthaṃ nṛsiṃha parameśvara||

Translation: Oh Nṛsimha, for your satisfaction, I now offer You divine, cool sandalwood paste mixed with camphor.

puṣpamantra

कालोद्भवानि पुष्पाणि तुलस्यादीनि वै प्रभा|

पूजयामि नृसिंहस्य लक्ष्म्या सह नमोऽस्तु ते||

kālodbhavāni puṣpāṇi tulasyādīni vai prabhā|

pūjayāmi nṛsiṃhasya lakṣmyā saha namo’stu te||

Translation: Oh Nṛsiṃha,I worship You, along with Laksmidevi with offerings of flowers that bloom in spring, and tulasi leaves. My humble obeisances unto You.

dhūpamantra

कालागुरुमयं धूपं सर्वदेवसुदुर्लभम्|

करोमि ते महाविष्णो सर्वकामसमृद्धये||

kālāgurumayaṃ dhūpaṃ sarvadevasudurlabham|

karomi te mahāviṣṇo sarvakāmasamṛddhaye||

Translation: O Mahāviṣṇu, just to fulfill all of my desires, I will worship You with and offering of black aguru, which is rarely available, even for the devas.

dīpamantra

दीपः पापहरः प्रोक्तस्तमस्यां राशिनाशनः|

दीपेन लभ्यते तेजस्म्तस्माद्दीपं ददामि ते||

dīpaḥ pāpaharaḥ proktastamasyāṃ rāśināśanaḥ|

dīpena labhyate tejasmtasmāddīpaṃ dadāmi te||

Translation: O Nṛsiṃha, by offering this ghee lamp, which destroys the darkness of ignorance, as well as all sinful reactions, one obtains special power. Therefore, I offer this ghee lamp to You.

naivedyamantra

नैवेद्यं सौख्यदं चान्तु भक्ष्यभोज्यसमन्वितम्|

ददामि ते रमाकान्त सर्वपापक्षयं कुरु||

naivedyaṃ saukhyadaṃ cāntu bhakṣyabhojyasamanvitam|

dadāmi te ramākānta sarvapāpakṣayaṃ kuru||

Translation: O beloved of Lakṣmī, I place before You this offering of naivedyam. May You be pleased with this offering and kindly remove all my sins.

arghyamantra

नृसिंहाच्युत देवेश लक्ष्मीकान्त जगत्पते|

अनेनार्घ्यप्रदानेन सफलाः स्युर्मनोरथाः||

nṛsiṃhācyuta deveśa lakṣmīkānta jagatpate|

anenārghyapradānena saphalāḥ syurmanorathāḥ||

Translation: O Lord Nṛsiṃha! O Acyuta! O Lord of the devas! O husband of Lakṣmī! O Lord of the universe, let all my desires be fulfilled by offering of this arghya to You.

pūjāmantra

पीताम्बर महाविष्णो प्रह्लादभयनाशकृत्|

यथा भूतार्चने नाथ योथोक्तफलदो भव||

pītāmbara mahāviṣṇo prahlādabhayanāśakṛt|

yathā bhūtārcane nātha yothoktaphalado bhava||

Translation: O Mahāviṣṇu, who wears yellow garments! O destroyer of fear for Prahlada, may You be satisfied with whatever little worship I offer You to the best of my ability, so that You bestow Your mercy upon me.

Final prayers before the visarjana of the murti

मद्वंशे ये नरा जाता ये जनिष्यति मत्पुरः|

तंस्त्वमुद्धर देवेश दुःसहाद्भवसागरात्|

madvaṃśe ye narā jātā ye janiṣyati matpuraḥ|

taṃstvamuddhara deveśa duḥsahādbhavasāgarāt|

Translation: O Lord of the devas, please deliver all those who have taken birth in my family, as well as those who will take birth in the future, from the intolerable ocean of material existence.

पातकार्णवमग्नस्य व्याधिदुःखाम्बुराशिभिः|

तीव्रैस्तु परिभूतस्य महादुःखगतस्य मे||

करावलम्बनं देहि शेषशायिन् जगत्पते|

श्रीनृसिंह रमाकान्त भाक्तानां भयनाशन||

pātakārṇavamagnasya vyādhiduḥkhāmburāśibhiḥ|

tīvraistu paribhūtasya mahāduḥkhagatasya me||

karāvalambanaṃ dehi śeṣaśāyin jagatpate|

śrīnṛsiṃha ramākānta bhāktānāṃ bhayanāśana||

Translation: O Lord who lies on the bed of Ananta Sesa! O Lord of the universe! O Nṛsiṃha! O husband of Lakṣmī! O destroyer of the devotees’ fear, I am suffering from great distress due to drowning in the ocean of sinful activities and disease. So, kindly lend me Your fearless hand and give me protection.

क्षीराम्बुधिनिवास त्वं प्रीयमाणो जनार्दन|

व्रतनेन मे देव भुक्ति मुक्ति प्रदो भव||

kṣīrāmbudhinivāsa tvaṃ prīyamāṇo janārdana|

vratanena me deva bhukti mukti prado bhava||

O Janārdana! O Lord who lies in the ocean of milk! O Supreme Lord, may You be pleased with my observance of this vow, and may You bestow upon me material enjoyment and liberation.

[Note:My main niggling problem with that page is the translation of deva=demigod and dānava=atheist. Dānavas are dānu’s sons…this is known from śruti firstly.]

Gopala Bhaṭṭa Gosvāmī here cites from mainly the Bṛhannārasiṃhapurāṇa and an unspecified āgama(simply saying ‘āgame’…).