Lord Kuber, who is considered treasurer of the riches of the world, is worshipped along with Sri Lakshmi, the Goddess of wealth. Traditionally Shri Kuber is worshipped during Lakshmi Puja on Amavasya day. However, Shri Kuber is also worshipped on Dhan Trayodashi during five days Diwali festivities.
If you have Murti or statue of Shri Kuber then it can be used for Puja. If you don't have Kuber Murti then as an alternate you can consider chest (Tijori, तिजोरी) or box of Jewelry, representing Shri Kuber itself and worship it. Before you start worshipping the chest, you should draw the sign of Swastik with Sindur and tie Moli (Kalaya) to it.
First of all one should meditate and remember Shri Kuber with following Mantra.
Var–Gade Dadhatam Bhaje Tundilam॥
Mantra Translation - I pray magnanimous Shri Kuber, Who mounts on human-form chariot, Who is master of all Nidhis (treasures) like great Garuda, Who is friend of Lord Shiva, Who is adorned with crown and other Jewelries and Who has one hand in Var-Mudra and carry Gada in the other hand.
After Dhyanam of Shri Kuber, invoke Him with following Mantra. While calling Shri Kuber your hands should be in Aavahan Mudra in front of the chest (Aavahan Mudra is formed by joining both palms and folding both thumbs inwards).
Aavahayami Dev! Tvamihayahi Kripam Kuru।
Kosham Vardhdaya Nityam, Tvam Pari–Raksha Sureshwar॥
॥ Shri Kuber–Devam Aavahayami॥
Mantra Translation - O Dev, Devo Ke Dev–Sureshwar! I’m inviting you. Please come and dwell here to oblige me. Please protect and enrich my treasure and its riches. Hence I invoke Shri Kuber.
3.Pushpanjali Asana (पुष्पाञ्जलि-आसन)
Once Shri Kuber has come to the chest, take five flowers in Anjali (by joining palm of both hands) and leave them in front of the chest to offer the seat to Shri Kuber while chanting following Mantra.
Aasanam Dev–Devesh! Preetyartham Prati-Grihyataam॥
॥ Shri Kuber-Devay Aasanarthe Pancha-Pushpani Samarpayami॥
Mantra Translation - It means–O Lord of Dev! Please accept the golden seat decorated with different types of jewels for my pleasure. Hence, I offer five flowers for the seat of Shri Kuber.
4.Nav Upchara Pujan (नव उपचार पूजन)
After this perform Shri Kuber Puja with Chandan, Akshata, Pushpa, Doop, Deep and Naivedhya while chanting following Mantras.
Om Shri Kuberaya Namha Padyom Padhyam Samarpayami।
Om Shri Kuberaya Namha Shirsi Arghyam Samarpayami।
Om Shri Kuberaya Namha Gandhakshatam Samarpayami।
Om Shri Kuberaya Namha Pushpam Samarpayami।
Om Shri Kuberaya Namha Dhoopam Ghrapayami।
Om Shri Kuberaya Namha Deepam Darshayami।
Om Shri Kuberaya Namha Naivedyam Samarpayami।
Om Shri Kuberaya Namha Achamaniyam Samarpayami।
Om Shri Kuberaya Namha Tamboolam Samarpayami।
5.Puja Samarpan (पूजन समर्पण)
After doing Pujan as described above, take Gandha, Akshata and Pushpa in left hand and leave them over or near the chest with right hand while chanting following Mantra.
Om Shri Kuberaya Namha।
Anen Pujanen Shri Dhanadhyaksha-Shri Kuber Preeyatam।
Mantra Translation - I convey my regards to Shri Kuber! I hope Shri Kuber would be pleased with my worship. I salute Him again and again.
It ends Shri Kuber Puja.