Theory:

Proper nouns are always capitalized. For example seven days of the week (Monday, Tuesday, Wednesday and so on) and the 12 months of the year (January, February, March and so on).
While we're at it, the name of the person who lives at this address, say, Jayram Dixit should also be capitalized, because it is a proper noun, too. Make sure that if you add the title "Mr" in front of Jayram Dixit, it should be capitalized too! Names of people, names of companies and names of specific brands are all proper nouns that are capitalized.
Capitalization rules: Though, while all proper nouns are capitalized, not all capitalized words are proper nouns. Following the rules for capitalization.
 
Take a look at the following examples to see capitalized words that aren't proper nouns.
Example:
1. My Indian neighbour likes to cook rice.
    ("Indian" might be a proper noun but in this example, it's not a noun. It's a proper adjective because it's modifying the word "neighbour").
 
2. If you want to drink a Kumbakonam coffee, go to Tamil Nadu.
    (Although "Tamil Nadu" is a proper noun, "Kumbakonam" is not. Again, it's a proper adjective because it's modifying the word "coffee").
 
3. Our teacher said, "The student will come out to greet you personally," but he never came.
    ("Our" is capitalized because it starts the sentence. "The" is capitalized because it starts the quote within the sentence. If the quote wasn't a complete sentence it wouldn't be capitalized).
Important!
Be sure to remember that while "I" is always capitalized, it's a pronoun, not a proper noun.