The concept of 33 koti devata in Hinduism!

Time and Worship

Time

In Hinduism, time follows the life of Brahma. The age of the world is reckoned in terms of one day in the life of Brahma, which is equivalent to 4,320,000,000 years. This period of time is divided into four yugas, which are reckoned in multiples of 432,000,000 years. Together these four yugas are called the Great Cycle. The world is now in the fourth and most degenerate stage, the Kali Yuga, which started in 3102 bce. The following two sites provide a fuller explanation: The Vedic Concept of Time and Brahma.
The annual calendar is lunar. But unlike the Moslem calendar, it is regularly adjusted to retain a rough equivalence with the solar year by adding an extra month. The numbering of the years goes according to two different systems called Vikram Samvant and Saka. The Vikram Samvant is more widely used. For a fuller explanation of the years, months and weeks, go here.
It is important to note that popular Hinduism holds that certain times are better for important events (marriage, business ventures, religious rites, etc.) than others. These times are different for different people and are calculated through a complex system based on the Vedas, the movements of the stars and planets, and the moon. In fact, each change in the moon's phase brings in a new moment. This is often carefully worked out. You can visit a site that depicts the moon phase at this precise moment.

Daily Worship

Daily worship in Hinduism usually takes place in three different places: in the home, in a temple, and/or at a street-side or road-side shrine.
The home of a religiously observant hindu is the location of two types of worship. First, there is the practice of rites that are probably older than the Vedas themselves. At dawn, the householder and his wife rise, purify themselves with a bath--usually in a temple pool or a river if one is available--and then make an offering to the fire-god Agni in their household fire. The man may then turn towards the rising sun and say a mantra to the sun-god Savatar, asking for blessing and understanding. A similar sequence of activities will take place in the evening.
Second, most hindu households have a small shrine to the gods important to that house. It may have a small statue of Krishna or a picture of Shiva or Durga. If the householder has a guru, a photo of the guru will appear, to remind the worshipper of the guru's teachings. This shrine will be the focus of household puja, i.e., worship. Offerings of food or drink may be laid before the statues, mantras and prayers may be said, and so on.
A nearby temple to a god or goddess is usually the focus of regular puja (i.e., worship). While a local temple may do for everyday worship, a grander cathedral-like, temple may be visited on special occasions. (To see pictures of a large Hindu temples, go here.) Offerings of meals, money, flowers, etc. may be brought by the devotee. Once the god has taken his part of the sacrifice, the devotee may share in some of the now-blessed food (called prasad). The worshipper may also say mantras, or listen to the priests chant, sing, or read from the sacred texts.
Within the temple, the god (such as Vishnu as Rama, or Ganesha) or goddess (perhaps Kali) will be treated as royalty--living royalty to be exact. The statue will be bathed and dressed, sometimes with sumptuous clothes for "holding court" other times with pajamas for sleeping. Meals and other gifts will be regularly given. During the god's or goddess' festival, the statue will be paraded through the streets. While some of this may seem silly to Western sensibilities, these actions help the worshippers view the divine being as immediately present. A mere statue does not need any special care, a statue revealing the divine presence does. For a description of how puja (worship) takes place during a long festival, visit this site.
Small shrines to hindu gods and goddesses, both major and minor, stand on road sides in the country and on the streets in cities. They may be permanently fixed and unattended, or on a cart and moved around by an attendant. During the day, as people pass by, they may stop, offer a short prayer or mantra, perhaps leave a small offering in gratitude for some blessing.

Festivals

Hindu festivals are based on the lunar calendar. In modern India, there are sixteen officially recognized holidays (when businesses close), although there are many more holidays than that. Most festivals are annual, but some happen on a longer cycle. The festival of Kumbha Mela, when millions of Hindus gather at the confluence of the Ganges and Jumna rivers takes place once every twelve years. For more information, go here.
Of the annual festivals, the two-day rites of Holi mark the end of winter and the beginning of spring. This celebration is linked to Krishna whose exploits with the gopis are reenacted. It is a time of gaity, joy, and hope for nature's rebirth. For a fuller discussion of Holi within Hinduism, go here.
In late summer, Krishna's birthday is celebrated at the Janmashtami.
Shortly afterwards, Ganesha is honored with the festival of Ganesh Charurti. To learn more about this festival, go here.
Sometime festivals that happen on the same day will be given different interpretations depending on whether the worshippers follow Shiva, Vishnu or the Sakti. In late September or early October, for instance, Shaivites and Saktites will celebrate the Durga Puja, while Vaishnavites will take part in the Dussehra, which celebrates Vishnu and his exploits as Rama in the Ramayana (and don't forget Hanuman!). Similarly, the Divali, which is the festival of lights, is celebrated either as the return of Rama from exile or as the puja of Lakshmi, the goddess of wealth and fortune. For a discussion of Divali (=Deepavali=Diwali) in Hinduism, visit this site.