The first puja, the Linga puja, was previously described.
Closer to midnight begins the second, the Rajasika puja. "Rajasika" means "passionate, active, dynamic." This puja is accompanied by mantras from the Puranas and right-hand Tantras. It is the most lavish worship with a plethora of offerings and gifts, accompanied by ecstatic singing, joy, and merriment. Prayers here focus on prosperity, wealth, glory, career, with personal (selfish) motivations in the guna of rajas (passion). But it doesn't necessarily mean that one has to ask Shiva for something. One can simply praise Him, savoring the very process of worshipping Him.
Tamasika Puja
The third phase (3rd puja) is Tamasika. Here, Shiva is worshipped in His fierce aspects, alongside His spouse Mahakali. Offerings for this puja are tamasic: strong beverages, wine, meat, fish, and heavy food types. Left-hand Tantra prayers and mantras are recited during this service. During this phase, one meditates upon Shiva's loyal warriors (shivaganas) dealing with anyone causing you troubles in life, chanting "Beat my enemy, beat! Devour, devour! Kill, kill! Expel, expel!" But in this context, an enemy might not necessarily be a particular individual but inner enemies, vices, and flaws. For example, offering a coconut (breaking it before the altar) symbolizes shattering one's ego, and the meditation is directed towards which qualities one would want to shatter within oneself. Much like a coconut, the ego has a sturdy, thick shell, but it's hollow inside. Pride, a sense of self-importance is as deceptive as a coconut: hard on the outside, but hollow and liquid inside. When a sacrificial animal is slaughtered, the meditation is about annihilating the beastly nature within us (the goat, rabbit, rooster are mere symbols). It's about our delusion, our ignorance. The animal's soul, having received a blessing, gets reborn in better forms, and the sacrificial meat will be prepared and distributed as a sacrament in the morning.
Fourth Puja
The last — the 4th puja — is about worshiping Shiva as Parashiva, the Absolute, beyond all qualities, names, and forms. What's important here isn't just the external worship but a deep meditation and discovery of inner unity with Shiva. The time of Brahma-muhurta, roughly between 3 to 5 a.m., is a pre-dawn time when a serene calm reigns in nature, conducive to such meditation. This is the time between sleep and wakefulness. It's believed that during this time, one can access the higher state of consciousness (turiya) and beyond (turiyatita) — that which is beyond thought, beyond the mind, where the immanent consciousness connects with the transcendent (Absolute, Divine). The fourth, final puja, offers an opportunity to perceive Shiva as the soul of your soul, your Higher Self. Here, a fire offering (agnihotra) is performed. Written prayers are burnt in the fire. They can be written in advance or during the ceremony. They are written in a polite form, for instance, "Oh, my dear beloved Lord Shiva! I am so-and-so. Please help me with this and that." Or simply, "Please notice me among everyone and show me some sign of Your grace, show that I mean something to You."
Conclusion
Throughout the night, continuous worship, veneration, and meditation take place. One should, at least for this time, free the mind from worldly thoughts. Retain only the name of Shiva and repeat, "Om namah shivaya" — "Om, homage to the Good One!". Strive to immerse completely in realization, in the spiritual experience. Forget the need for sleep, food, and drink. Forget about the physical. This Night offers unique opportunities.