I want to know how does he influence our lives. How does he involve himself?
Lord Narayana is the lord of the universe. He is the source of all creation. He is considered as supreme brahman in hinduism. Its Lord Narayana from whom the whole universe is manifested.
The role and significance of Lord narayana in our personal lives is that we have to worship him in order to get liberated from bondage of this sansara i.e. cycle of births and deaths . As To attain moksha is the highest goal of our lives according to shastras. Lord Narayana is also protector of our Pranas .
So Lord Narayana is the highest reality in our lives , which we have to know. He is destroyer of the sins as well as bestower of salvation to us.
The role of Lord Narayan is describes in Narayana Suktam . He is describes as destroyer of our sins.
विश्वतः परमान्नित्यं विश्वं नारायणं हरिम् ।
विश्वं एव इदं पुरुषः तद्विश्वं उपजीवति ॥
This universe is the Supreme Being (Purusha) alone; hence it subsists on That, the Eternal which transcends it (in every way), -the omnipresent Absolute which destroys all sins.
Lord Narayana is also the truth of our lives , he is the law with which we operate , work and do various things in this world. What this mean is all this we are experiencing (pleasures , pain etc.) is because of Lord Narayana himself.
ऋतं सत्यं परं ब्रह्म पुरुषं कृष्ण पिङ्गलम् ।
ऊर्ध्वरेतं विरूपाक्षं विश्वरूपाय वै नमो नमः ॥
Prostrations again and again to the Omni-Formed Being, the Truth, the Law, the Supreme Absolute, the Purusha of blue-decked yellow hue, the Centralised-Force, Power, the All-Seeing One.
Apart from that Srimad Bhagavata Purana is also telling us about Narayana. Here below shloka is telling us the highest goal of our lives is Narayana.
नारायणपरो योगो नारायणपरं तपः ।
नारायणपरं ज्ञानं नारायणपरा गतिः ॥SB 2.5.16॥
nārāyaṇa-paro yogo nārāyaṇa-paraḿ tapaḥ
nārāyaṇa-paraḿ jñānaḿ nārāyaṇa-parā gatiḥ
All different types of meditation or mysticism are means for realizing Narayana. All austerities are aimed at achieving Narayana. Culture of transcendental knowledge is for getting a glimpse of Narayana, and ultimately salvation is entering the kingdom of Narayana.
There is also a Raksha mantra in Srimad Bhagavata Purana which tells us that Lord Narayana is the protector of our prana. i.e. our life force or our vital breath.
इन्द्रियाणि हृषीकेश: प्राणान नारायणोSवतु ||
श्वेतद्विपपतिच्श्रीतं मनो योगेश्वरोSवतु ||SB 10.6.24 ||
indriyāṇi hṛṣīkeśaḥ prāṇān nārāyaṇo 'vatu
śvetadvīpa-patiś cittaḿ mano yogeśvaro 'vatu
May Hrsikesa protect Your senses, and Narayana Your life air. May the master of Svetadvipa protect the core of Your heart, and may Lord Yogesvara protect Your mind.
So ultimately Lord Narayana is highest truth of our lives , he is bestower of moksha to us , protecting ourselves in our lives and is the vital breath i.e. our prana itself , destroying our sins , its because of him we are here at first place.