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.
मनुज-बाह्य-विमान-स्थितम्,
गरुड-रत्न-निभं निधि-नायकम्।
शिव-सखं मुकुटादि-विभूषितम्,
वर-गदे दधतं भजे तुन्दिलम्॥
Manuj-Brahma-Viman-Sthitam,
Garuda-Ratna-Nibham Nidhi-Naykam।
Shiva-Sakham Mukutadi-Vibhushitam,
Vara-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).
आवाहयामि देव! त्वामिहायाहि कृपां कुरु।
कोशं वर्द्धय नित्यं त्वं परि-रक्ष सुरेश्वर॥
॥श्रीकुबेर-देवम् आवाहयामि॥
Avahayami Deva! Tvamihayahi Kripam Kuru।
Kosham Varddhaya Nityam Tvam Pari-Raksha Sureshwara॥
॥ Shri Kuber-Devam Avahayami ॥
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.
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.
नाना-रत्न-समायुक्तं कार्त्त-स्वर-विभूषितम्।
आसनं देव-देवेश! प्रीत्यर्थं प्रतिगृह्यताम्॥
॥श्रीकुबेर-देवाय आसनार्थे पञ्च-पुष्पाणि समर्पयामि॥
Nana-Ratna-Samayuktam Kartta-Swara-Vibhushitam।
Asanam Deva-Devesha! Prityartham Prati-Grihyatam॥
॥ Shri Kuber-Devaya Asanarthe 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.
After this perform Shri Kuber Puja with Chandan, Akshata, Pushpa, Doop, Deep and Naivedhya while chanting following Mantras.
ॐ श्रीकुबेराय नमः पादयोः पाद्यं समर्पयामि।
ॐ श्रीकुबेराय नमः शिरसि अर्घ्यं समर्पयामि।
ॐ श्रीकुबेराय नमः गन्धाक्षतान् समर्पयामि।
ॐ श्रीकुबेराय नमः पुष्पं समर्पयामि।
ॐ श्रीकुबेराय नमः धूपम् आघ्रापयामि।
ॐ श्रीकुबेराय नमः दीपं दर्शयामि।
ॐ श्रीकुबेराय नमः नैवेद्यं निवेदयामि।
ॐ श्रीकुबेराय नमः आचमनीयं समर्पयामि।
ॐ श्रीकुबेराय नमः ताम्बूलं समर्पयामि।
Om Shri Kuberaya Namah Padayoh Padyam Samarpayami।
Om Shri Kuberaya Namah Shirasi Arghyam Samarpayami।
Om Shri Kuberaya Namah Gandhakshatan Samarpayami।
Om Shri Kuberaya Namah Pushpam Samarpayami।
Om Shri Kuberaya Namah Dhupam Aghrapayami।
Om Shri Kuberaya Namah Dipam Darshayami।
Om Shri Kuberaya Namah Naivedyam Nivedayami।
Om Shri Kuberaya Namah Achamaniyam Samarpayami।
Om Shri Kuberaya Namah Tambulam Samarpayami।
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.
ॐ श्रीकुबेराय नमः।
अनेन पूजनेन श्रीधनाध्यक्षः श्रीकुबेरः प्रीयताम्।
नमो नमः।
Om Shri Kuberaya Namha।
Anena Pujanena Shri Dhanadhyakshah Shri Kuberah Priyatam।
Namo Namah।
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.