In Caribbean Shaktism, most prayers for Madrassi deities like Madurai Veeran, Kateri, Sangili Karuppar, Muniswaran, etc. aren't done much at home. When they are, mantras are rarely said, it usually is just the singing of devotional chants while thappus drum and the devotee/priest cuts the various balidaan (non-blood sacrificial) fruits, offers incense, cigars (if the deity likes cigars), alcohol libations into the half of a coconut (again, if the deity likes it), aarti by putting a lit camphor into the half of a coconut or on a lime, the sprinkling of manjal tanni to consecrate the space, the circling of sambrani and camphor around the altar 7 times, before then pouring dhaar at the end of the puja onto the floor and touching the lota and putting it to your head and then prostrating. Then after, people eat the offerings. But, Sanatani deities do have their pujas done at home and they are usually done with mantras, and other such items. I just wanted to disclaim that because you wont see any puja vidhis for these deities since no mantras are said during their prayers, just chants like the Mariamman Thalattu, the Madurai Veeran Arul Stuthi, devotional songs, the Kali Thalattu, the Amman Virutham, the Kamakshi Virutham, the Lalita Sahasranama, etc. 

I also include the offerings for the deity at the end of the post for the "Who Is" series, so use that as a reference.

Shodashopachara Puja for whatever deity: https://www.hinduamerican.org/blog/hindu-puja-instructions

Poorvangam (Steps to take before doing a ritual, any unknown terms should be in resources, if not, feel free to contact me to ask questions)- https://stotranidhi.com/en/puja-vidhanam-poorvangam-in-english/

Hardidra Vinayaka Pujai (Puja done to Ganesh made out of turmeric, always done before a Puja): https://stotranidhi.com/en/sri-haridra-ganapati-puja-in-english/

Ganesh Puja Vidhi (For Ganesh Chaturthi or other like holidays):
https://www.drikpanchang.com/hindu-gods/ganesha/puja-vidhi/lord-ganesha-puja-vidhi.html

Saraswati Puja Vidhi:
https://www.drikpanchang.com/hindu-goddesses/saraswati/puja-vidhi/shodashopachara/saraswati-puja-vidhi.html

Latchmi Puja Vidhi:
https://www.drikpanchang.com/festivals/lakshmipuja/info/lakshmi-puja-vidhi.html

Sivan Puja Vidhi:
https://www.drikpanchang.com/hindu-gods/trimurti/lord-shiva/info/puja-vidhi/lord-shiva-puja-vidhi.html

Sitaram Puja Vidhi (For Rama Navami):
https://www.drikpanchang.com/hindu-gods/trimurti/lord-shiva/info/puja-vidhi/lord-shiva-puja-vidhi.html

Krishna/Govinda Puja Vidhi (For Krishna Janmashtami):
https://www.drikpanchang.com/dashavatara/lord-krishna/janmashtami/puja-vidhi/krishna-janmashtami-puja-vidhi.html

Anjaneya (Hanuman) Puja Vidhi:
https://www.drikpanchang.com/hindu-gods/hanuman/puja-vidhi/hanuman-puja-vidhi.html

Durga Maa Puja Vidhi:
https://www.drikpanchang.com/navratri/durga-puja/puja-vidhi/durga-puja-vidhi.html
(Durga Paath prayers done during Navrathri) https://dipika.org.za/wp-content/uploads/2020/04/D.I.Y-Durga-Paath-Saptashati-Puja-and-Havan.pdf

Satyanarayana Puja Vidhi (Done on Purnima, or full moon):
https://www.drikpanchang.com/hindu-gods/trimurti/lord-vishnu/puja-vidhi/satyanarayan-puja-vidhi.html

Mariamman Puja Vidhi (For the whole month of Aadi):
1. (This is good for a very simple puja set up) https://kailaskitchen.blogspot.com/2009/07/maa-vilakku-pooaji-paachai.html?m=1

2. (Elaborate Puja Vidhi)
Click Here: Mariamman Puja Vidhi

Kaliamman Puja Vidhi:
https://dipika.org.za/wp-content/uploads/2020/01/Mother-Kali-Symbolic-Bali-Non-blood-Daan-Prayers.pdf

Kannimar Pujai Vidhi (Puja done to the seven goddesses, this is done traditionally when someone catches an illness due to karma, caused by the kannimar): 
https://dipika.org.za/wp-content/uploads/2016/07/Kannimaar-Prayers-%E2%80%93-The-Seven-Fairies-Prayers.pdf

Navgraha Puja Vidhanam:
https://dipika.org.za/392-2/

Dee Baba and Dee Mata Puja Vidhi:
https://dipika.org.za/wp-content/uploads/2023/04/The-Importance-of-Dee-Baba-worship-in-Hinduism-Sanatan-Dharma-1.pdf

Murugan Puja Vidhi:
https://www.docdroid.net/ewSk4rH/subramanya-puja-final-pdf

Kamakshi Puja Vidhi:
https://stotranidhi.com/en/sri-lalitha-shodasopachara-puja-vidhanam-in-english/

Varahi Puja Vidhi:
https://stotranidhi.com/en/sri-varahi-devi-shodasopachara-puja-in-english/

Kateriamman and Muniswaran Puja Vidhi (for a new mother/child):
https://tamilculture.com/devi-ma-johannesburgs-authority-on-katheri-prayer
Although this specific ritual is how South Africans perform it, she is the same goddess everywhere, so it doesn't matter.

How-to Havans (Fire Ritual) for various deities:
Narayana Havan- https://www.vedicastrologer.org/homa/regular/vishnu_r_eng.pdf
Sri Krisna Havan- https://www.vedicastrologer.org/homa/regular/krishna_r_eng.pdf
Vinayagar Havan- https://www.vedicastrologer.org/homa/regular/ganapati_r_eng.pdf
Subramanya Havan- https://www.vedicastrologer.org/homa/simple/kartikeya_s_eng.pdf
Anjaneya Havan- https://www.vedicastrologer.org/homa/regular/hanuman_r_eng.pdf
Sangar Havan- https://www.vedicastrologer.org/homa/regular/shiva_r_eng.pdf
Kal Bhairo Havan-https://www.vedicastrologer.org/homa/regular/kala_bhairava_r_eng.pdf 
Lakshmi Havan- https://www.vedicastrologer.org/homa/regular/mahalakshmi_r_eng.pdf
Saraspadi Havan- https://www.vedicastrologer.org/homa/simple/saraswati_s_eng.pdf
Durgai Havan- https://www.vedicastrologer.org/homa/simple/durga_s_eng.pdf
Kamatchi Havan- https://www.vedicastrologer.org/homa/simple/lalita_s_eng.pdf
Chandi Homa- https://www.vedicastrologer.org/homa/regular/chandi_r_eng.pdf
Kaliamman Homa- https://www.vedicastrologer.org/homa/simple/kaali_s_eng.pdf
Navgraha Homa- https://www.vedicastrologer.org/homa/simple/navagraha_s_eng.pdf
Suryan Homa- https://www.vedicastrologer.org/homa/simple/surya_s_eng.pdf
Naga Devta Homa- https://www.vedicastrologer.org/homa/simple/naaga_s_eng.pdf
Ancestor Homa- https://www.vedicastrologer.org/homa/simple/pitri_s_eng.pdf

How-to Videos-
Ganesh Puja Vidhi: https://www.youtube.com/watch?v=0auqeeLs9fg
Saraswati Puja Vidhi: https://www.youtube.com/watch?v=uxnCdnxK4_o&t
Diwali Puja Vidhi: https://www.youtube.com/watch?v=MV4VPXdjw80
Navarathri Puja Vidhi: https://www.youtube.com/watch?v=5yEklgZX8hc&t
Shiva Puja Vidhi: https://www.youtube.com/watch?v=6BfFuXDeCG4
How to offer Durga Dhaar: https://www.youtube.com/watch?v=gBF6_8yjEy8
Hanuman Puja Vidhi: https://www.youtube.com/watch?v=Yu1EYsltX8M
Pitri Paksh (Ancestor Prayers) Puja Vidhi: https://www.youtube.com/watch?v=0FXFYfkUS84&t

Set-up videos:
Gangai Amman set-up: https://www.youtube.com/watch?v=EMYpvaNPfSw
General Puja set-up: https://www.youtube.com/watch?v=pXNKip35Isc&t
Shiva Puja set-up: https://www.youtube.com/watch?v=_n4YIXQNH7s&t
Hanuman Puja set-up: https://www.youtube.com/watch?v=aetD-u0bivU&t
Diwali Puja set-up: https://www.youtube.com/watch?v=-pNEKgdasAw
Navgraha Puja set-up: https://www.youtube.com/watch?v=sGLPhIKS4Zw
Satyanarayan Puja set-up: https://www.youtube.com/watch?v=lA_2wy0Sxmc
Navarathri Puja set-up: https://www.youtube.com/watch?v=O9O4hUqtYyE&t

The most simple and common way to do a pujai is simply to lay down the offerings in front the deity, offer the deity chandan, kumkum, and haldi on their forehead, light a diya or two vilakku, then sing devotional songs or recite sacred scripture (such as the Lalita Sahasranamah for any Devi, the Mariamman Thalattu for Kali and Mariamman, the Hanuman Chalisa for Hanuman, the Amman Virutham for Mariamman, the Vishnu Sahasranama for Narayana, etc.) and then end with aarti for the deity while there is drumming, the ringing of bells, or simply just singing devotional aarti songs such as "Jai Jagdish Hare" or "Jai Ganesh Deva". At the end of the aarti, people cup their hands over the fire and pass it over their head to take the blessings of the deity, then prostrate before the deity, and then eat the prasadam offered.