Puja is worship of the Lord. This is one of the nine modes of Bhakti. This is also called Archana. The Lord is worshipped either in His Nirguana or Saguna aspect. Even this worship is done either with external materials or merely mentally in the case of advanced devotees.
The Bhakta does Puja to his Ishta-Devata. The Puja is Vedic, Tantric or mixed as is suitable to the devotee. One may choose any method according to his liking.
Take bath in the morning. Perform your daily Sandhya or prayer. If there is an idol of the Devata it is good. Otherwise, worship can be done on the floor itself, after cleaning the place and drawing a Mandala there. Collect flowers, Dhoop, scented sticks, sandal paste, Arati (Dipa), camphor, fresh water, food-offerings (Bhog) to the Lord, a clean seat to sit on, a small bell, conch and cymbals if available.
Offer a prayer to the Lord with Bhava and devotion. Offer flowers or rice soaked in water with Kumkum (Akshata) to the Lord with His hundred and eight names or His Mula-Mantra repeated hundred and eight times. Offer Abhisheka with fresh water or milk or ghee or honey or Panchamrita as is convenient. Read elevating Stotras or portions of Bhagavata, Ramayana, etc., concerning the glories and Lilas of Bhagavan. If possible do Sahasranama Archana. Offer Arghya, Padya, Neerajana, etc. Mentally always think of the form of the Lord.
You should not get up in the middle of the Puja for collecting anything. Keep ready everything beforehand. As many Mantras, Stotras and prayers as possible should be repeated to kindle divine emotion. You should decorate the Lord with fresh clothes and garlands made of flower. Adore Him with ornaments, flowers, scent, sandal paste etc. Do it with intense love and devotion.
Offer to the Lord as Bhog sweet, cooked rice or some food that can conveniently be offered. Food specially prepared with ghee, milk etc., and those prepared with curd, vegetables, butter are very much recommended.
The image should be rubbed with oil, cleaned, adorned and given all such loving treatment which one would give to his most beloved and dearest being in the world. Prepare various kinds of dishes for Bhog if possible and arrange for music, singing and dancing with divine Bhava on special days.
Do Mahapuja. Offer Arati, burn camphor, wicks dipped in ghee etc. Let there be singing of the Lord's glories and chanting of His Names. Offer prayers and surrender yourself to the Lord. Hear stories of the Lilas of the Lord as recorded in the scriptures. Say, O Lord! Have mercy on me. Be gracious unto me.
Place your head on the Lord's feet and pray, O Lord! Protect me from the ocean of Samsara with the shark of death in it. I am terribly afraid of it. I have taken shelter in Thee.
Offer Prasad to others. If possible feed some poor people every day. Give Dakshina. Give clothing. Worship the poor as the Lord.
Do everything with Nimitta Bhava. Have no selfish desires behind the worship you do.
Manasika Puja is doing worship of the Lord without any external materials. All materials necessary for Puja are imagined in the mind and you feel that you are offering all of them to the Lord as in formal worship. This is more powerful than external worship. For, concentration is more in Manasika Puja than in Bahya Puja.
Mentally feel all that you do in external worship. Enthrone the Lord in your heart. Do Puja, offer Arati, Arghya etc. mentally. Do Shodasopachara-Puja mentally. This is only a feeling of what is otherwise done actually with hands. Feeling is more effective than action.
Para Puja is the highest kind of worship. This is the worship of the Jnanis. This is the effect of Realisation of the Self. The devotee feels that he can do nothing but only experience God. He says:
O Lord! How can I worship Thee who is without parts, who is Existence itself? How can I pray to Thee when Thou art my very being itself? How can I offer Arghya, Padya etc. to Thee when Thou art ever pure? How can I offer anything to Thee when Thou art ever an Apta-Kama? Can I wave a candle to the Sun and can I bathe the ocean with a glass of water? How can I offer Bhog to Thee when Thou art self-contented? And in this way the devotee feels the Infinite Nature of God. Para Puja is thus an illustration of impossibility of formal worship to God in consideration of His infinite and Eternal Nature full of Knowledge and Bliss. Para Bhakti and Para Puja belong to the same stage. At this stage the devotee becomes one with God and loses his individuality.