How can we worship Shri Krishna at home? Is it enough to install an idol, or are there other rituals that are mandatory?

begin with the simple and basic 4 Regulative Principles set out by

the Gaudiya Vaishnavas or in general by all Vaishnavas ;

This is just my own opinion.

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1. no meat-eating (including onion, garlic, eggs, mushrooms, carrots?),

Dheepam samarpayami

5. Offer Naivedhyam ( food and drink offerings )

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Dhoopam samarpayami

4. Offer Dheepam ( one edible desi ghee oil lamp and one pure edible sesame oil lamp )

In my opinion , anyone can worship Shri Maha Vishnu ( Naaraayana ) and Shri Lakshmi Devi. To gatekeep and to prevent others from worship and bhakthi is nonsensical. Shri Maha Vishnu Naaraayana and Shri Lakshmi Devi are not so uptight as us humans. If you look carefully at the images and artwork of Shri Maha Vishnu , he embodies all opulences , beauty, grace and powers. He is also a flamboyant archtype . . not as rigid as what others made him out to be.

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4. and no gambling (pretty obvious as this is additive forming)

2. Offer Pushpham ( fresh fragrant flowers such as jasmine and red roses )

Meditate and do japa and feel the immense blessings Shri Shri Maha Vishnu Naaraayana and Shri Lakshmi Devi brings forth. May Lord Shri Krishna and Shri Radhe blesses you.

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But if you are serious about following a spiritual path and journey ;

Naivedhyam samarpayami

2. no illicit sex (only for serious marriage, procreation and love; not for one night stands),

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Gandham samarpayami

3. Offer Sugandham Dhoopam ( incense cone known as dhupa or incense stick known as agarbatti )

The most important thing here is faith , love and devotional service. Shri Krishna is not someone whose hell bent on my way or the highway or an extremely strict disciplinary master or a psychopath. In whatever mood and approach one does, he or she or they will come to me thus Shri Krishna does not care about our measly offerings and stinking bodies even if we shower a billion times in the Ganges River. What wins him over is your faith, love and devotional service. And also with how you treat others.. if you see that Shri Krishna is in all beings , then love flows naturally and you will feel naturally blessed.

We can't afford AC and its so hot, theres literally pools of sweat on the couch (TMI sorry) what can I do? I have a ceiling fan but my room feels still feels like a sauna. Any tips to stay cool? I can't fall asleep at night😭

Pushpham samarpayami

Jai Hind, Jai Shri Raam , Jai Shri Krishna.

3. no intoxication (no tea, no coffee, no chocolates, no alcohol , no narcotics and no cigarettes),

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Om Shri Krishnaya Namaha ,

So worship away in happiness and gladness, learn how to do the simple panchoupachara puja.

1. Offer Gandham ( sandalwood paste to the picture of statue )

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But. . . to be honest with you , a lot of Vaishnavas in India and South East Asia that I know personally , at home cooks with onion, garlic, carrots . . . so yeah . . . they only avoid eggs, meat, cigarettes, alcohol and illicit sex..