Left and Right politics in India

Broad ideology:

Since the French revolution, political parties across the world are categorized into left & right. Originally it used to mean the seating arrangement in Estates General of France (people who sat on the right supported monarchy and people on the left sympathized with the revolutionaries). 

Left: Parties that support communism/socialism. Sometimes they have a progressive outlook towards science & social values, but have a huge suspicion on businesses. They want government's involvement in businesses & economy, but not as often on the society (civil liberties). CPI and CPI (M) kind of lefties, although they don't believe that much in civil liberties. 

Right: Parties that are conservative and believe in the traditional values. They believe in religion, businesses and capitalism. They want government's involvement in society, but not businesses. BJP is on the right.

No major ideology: This encompasses all the rest of Indian parties. Usually they are anti-business and thus bucketed into the "center-left" category meaning they are a confused lot who sometimes side the left. Congress falls in it.

Size and Spread:

In India, if a party has a sizable presence in 4 or more states, it is considered a national party. There are officially 6 of them in India now: Congress, BJP, Communist Party of India (CPI), Marxist Communist Party (CPI M), Bahujan Samaj party and Nationalist Congress party. Although there are 6 official national ones, only two are considered truly national by common society: Congress and the BJP.  
Beyond the 6 national parties, there are a few hundred regional parties. These parties primarily appeal to their own region/language. For instance, DMK/AIADMK believe in Tamil superiority and Trinamool Congress does the same for Bengalis. Regional parties are in general, far more corrupt than the national ones. 

Major Parties

Congress Party:  A center-left party that was founded by legendary men & women in 1885. To compensate for the positives of the great leaders of the past, the party has elected Ms. Sonia Gandhi. On a more serious note, Congress is dominated by people closely associated with past leaders (sons, grandsons, in-laws, assistants, chamchas). Positives: The party has a better record in avoiding caste-politics and is slightly neutral when it comes to religion. 

Bharatiya Janata Party: An offshoot of RSS (a rightwing social unit), BJP is a party that rose to power in the 1980s to represent the middle class & conservative Hindus. Somewhere they lost the way and have become a confused lot, torn between pro-business units and pro-Hindutuva units. Many of their new crop of leaders are clean and agile (such as a CMs of Goa and Chattisgarh). Given its conservative stance on a few issues, it is the party that Indian media loves to bash the most. Disparagingly called the Brahmin-Baniya Party, although the party has recently brought more of other castes. Positives: The party has a good development record and tries to avoid regional fightings.

Communists: They are traditionally dominant in the states of Kerala, West Bengal and Tripura. Mainly backed by worker unions, student organizations and confused elites. They are typically anti-business and anti-West.  Positives: Arguably they are pro-environment and worker rights.