I've spoken before about temples, called Mandir. Home worship is also an important part of Hinduism.
Hindu homes have shrines in them and these are often called the heart of the Hindu home.
Some go to Mandir every day, others go only to request particular things or to have a particular ritual done. These rituals are called pujas and there are simple ones that can be done at home and there are very complex ones requiring certain ingredients and mantras. There are different pujas for different occasions and for different deities.
At home the puja will usually consist of ringing a bell, lighting incense, circling a light in front of the deities (called arti), and offering fruit, flowers, and/or a mix of rice and tumeric. Sometimes the deities are bathed in water or in milk or other substances and clothed. Red kumkum powder is put on the forehead of the deity with the thumb of the right hand and the same is applied to the forehead of the devotee. Often bhajans, worship songs, will be sung or played.
A house's shrine may be an entire room, or a niche in the wall. There are small metal temples sold that one can use to house murtis (statues of the gods). The gods themselves will be ones that are connected to the region or the family. Individuals are encouraged to find a god who inspires them in particular.
I have yet to see a shrine that did not include Ganesha. He is the most beloved god and is called "the remover of obstacles." He is prayed to before starting anything new.
Puja is performed everyday. The food that was offered is shared with the members of the family. It is called prasad and is considered to be blessed. This food is consumed before any other food of the day. Also, the flowers that are offered in the puja cannot be sniffed ahead of time. The flowers' first fragrance belongs to the gods.
Tradition has it that the puja is performed at sunrise by the ladies of the household. Before it begins, they must be bathed and cleanly dressed. I will admit, I don't get up that early to do it! (Although my parents for the last thirty years have meditated for 30 minutes at every sunrise and sunset, these times of day are supposed to be filled with spiritual energy).
Cleanliness is very important in Hinduism. The right hand, considered more clean, is used for eating and for other things. Shoes are removed before entering a sacred space such as a Mandir, and because of home shrines, shoes are removed when entering a Hindu home.
Another religious practice done in the home is the blessing of new things. The home itself and big purchases like cars are blessed by a priest, who comes to the home for the ritual.
I am lucky enough in my new apartment to have a separate space for my shrine. Our one bedroom apartment came with two closets, a walk-in one and a small one. I commandeered the smaller one and set up my murtis, pictures, incense, lights, etc. I have a CD of bhajans to play. I close myself in that closet each day and perform my own simple puja.
Some different examples:
More information is available at these websites:
A discussion among young American Hindus about gods and worship:
I like this one because it is white people doing it!
Other examples of pujas, by searching for "home puja" at YouTube:
UPDATE ON LIFE:
This weekend my boyfriend and I are flying to my parents' house for my birthday. I will not be wearing my bindi. I plan to deal with that with them at my brother's graduation in May. I will, however, have the chance to practice some Hindi with my mother's Indian friends. Very excited for that.
I've started doing www.livemocha.com for Hindi learning as well. One of my friends likes it better than Rosetta Stone. I still prefer Rosetta Stone, but I think LiveMocha is a great next step. It has you write and speak exercises, which get reviewed by native speakers. For some reason, though, they feel the need to bash Rosetta Stone and that upsets me. I love Rosetta Stone so much, and I'm very protective of it! LiveMocha is free, at least for the earlier lessons.
Also, my boyfriends family has been made aware of my religion. I've heard this third hand, but apparently, after he and I left at Easter, someone asked what religion I was. His mother planned to just say she didn't know, but his stepfather jumped in to say I was Hindu. Apparently, his grandmother's eyes got huge. They have to find out eventually and probably better for them to start getting used to it now rather than later. His immediate family is very open minded about it and his mother even gave me a gift certificate to India Sari Palace for my birthday!