Goddess Saraswati who is considered as the goddess of knowledge and arts is worshipped during Diwali Puja, Navratri Saraswati Puja and Vasant Panchami. In Gujarat, Saraswati Puja during Diwali is also known as Sharda Puja and Chopda Puja.

To begin Saraswati Puja, Bahi-Khate i.e. account books are kept at the place of worship. A Swastika symbol should be drawn on account books with Rochana or red Sandal paste. Once Swastika is drawn on account books, Saraswati Puja can begin.

Dhyana (ध्यान)
Puja should begin with the meditation of Bhagawati Saraswati. Dhyana should be done in front of Bahi-Khate symbolically representing Goddess Saraswati. Following Mantra should be chanted while meditating on Bhagawati Saraswati.
Saraswati Pujan
Shri Saraswati Puja during Diwali
Dhyana Mantra

Ya Kundendu-Tushara-Hara-Dhavala, Ya Shubhra-Vastravrita,
Ya Vina-Vara-Danda-Mandita-Kara, Ya Shveta-Padmasana॥
Ya Brahmachyuta-Shankara-Prabhritibhirdevaih Sada Vandita,
Sa Mam Patu Saraswati Bhagawati Nihshesha-Jadyapaha॥
मन्त्र अर्थ – जो कुन्द-पुष्प और हिम-माला के समान उज्जवल-वर्णा हैं, जो उज्जवल वस्त्र-धारिणी हैं, जो सुन्दर वीणा-दण्ड से सुशोभित कर-कमलोंवाली हैं और जो सदा ब्रह्मा-विष्णु-महेश आदि देवताओं द्वारा वन्दिता हैं, वे जड़ता को निर्मूल करनेवाली भगवती सरस्वती मेरी रक्षा करें।
Avahan (आवाहन)
After Dhyanam of Bhagwati Saraswati, invoke Her in front of Bahi-Khate with following Mantra. While calling Bhagwati Saraswati your hands should be in Avahan Mudra in front of Bahi-Khate (Avahan Mudra is formed by joining both palms and folding both thumbs inwards).
Avahan Mantra

Agachchha Deva-Deveshi! Tejomayi Saraswati!
Kriyamanam Maya Pujam, Grihana Sura-Vandite!
॥Shri Saraswati-Devim Avahayami॥
मन्त्र अर्थ – हे देवताओं की ईश्वरी! तेज-मयी हे देवि, सरस्वति! हे देव-वन्दिते! आइए, मेरे द्वारा की जानेवाली पूजा को स्वीकार करें।
॥मै भगवती सरस्वती का आवाहन करता हूँ॥
Pushpanjali Asana (पुष्पाञ्जलि-आसन)
Once Bhagwati Saraswati has come after invoking, take five flowers in Anjali (by joining palm of both hands) and leave them in front or near Bahi-Khate to offer the seat to Bhagwati Saraswati while chanting following Mantra.
Pushpanjali Mantra

Nana-Ratna-Samayuktam, Karta-Swara-Vibhushitam।
Asanam Deva-Deveshi! Prityartham Prati-Grihyatam॥
॥Shri Saraswati-Devyai Asnarthe Pancha-Pushpani Samarpayami॥
मन्त्र अर्थ – हे देवताओं की ईश्वरी! विविध प्रकार के रत्नों से युक्त स्वर्ण-सज्जित आसन को प्रसन्नता हेतु ग्रहण करें।
॥भगवती सरस्वती के आसन के लिए मैं पाँच पुष्प अर्पित करता हूँ॥
Nav Upchara Pujan (नव उपचार पूजन)
After this perform Bhagwati Saraswati Puja with Chandan, Akshata, Pushpa, Dhoop, Deep and Naivedhya while chanting following Mantras.
Bhagawati Saraswati Pujan Mantra

Om Shri Saraswati-Devyai Namah Padayoh Padyam Samarpayami।
Om Shri Saraswati-Devyai Namah Shirasi Arghyam Samarpayami।
Om Shri Saraswati-Devyai Namah Gandhakshatam Samarpayami।
Om Shri Saraswati-Devyai Namah Pushpam Samarpayami।
Om Shri Saraswati-Devyai Namah Dhupam Ghrapayami।
Om Shri Saraswati-Devyai Namah Dipam Darshayami।
Om Shri Saraswati-Devyai Namah Naivedyam Samarpayami।
Om Shri Saraswati-Devyai Namah Achamaniyam Samarpayami।
Om Shri Saraswati-Devyai Namah Tambulam Samarpayami।
Puja Samarpan (पूजन समर्पण)
After doing Pujan as described above, take Gandha, Akshata and Pushpa in left hand and leave them over or near Bahi-Khate with right hand while chanting following Mantra.
Bahi Khata Pujan Mantra

Om Shri Saraswatyai Namah। Anena Pujanena Shri Saraswati Devi Priyatam। Namo Namah।
मन्त्र अर्थ – श्रीसरस्वती को नमस्कार। इस पूजन से श्रीसरस्वती देवी प्रसन्न हों, उन्हें बारम्बार नमस्कार।