A proper noun is a noun which names a specific person, place, or thing.
Proper nouns are capitalized. That includes the following categories of names:
Each part of a person's name:
James A. Garfield Chester Alan Arthur
Given or pet names of animals:
Lassie Trigger Secretariat
Geographical and celestial names:
Red Sea Alpha Centauri Lake Havasu City
Monuments, buildings, meeting rooms:
the Taj Mahal Grant's Tomb Room 222
Historical events, documents, laws, and periods:
the Civil War the Hatch Act the Reformation
Months, days of the week, holidays:
Monday Easter December
Groups and languages:
Myopia Hunt Club the Republicans Israeli French National Football League
Religions, deities, scriptures:
God Christ the Bible the Torah Islam
Awards, vehicles, vehicle models, brand names:
the Nobel Peace Prize Eagle Scout Ford Escort the Bismarck Kleenex
Some parts of last names may not be capitalized.
Sometimes the part of the last name following Mac (but never Mc or M') may not be capitalized. For example, Prime Minister J. R. MacDonald, but author George Macdonald. There is no rule, just learn the name.
Sometimes the part of the last name following the particles de, du, d', den, der, des, la, le, l', ten, ter, van, or von (and similar particles) may or may not be capitalized. The particles themselves may or may not be capitalized. Check to see how the person prefers it.
The spelling rule in Europe, where such particles are more common, is not to capitalize the particle when the first name is being used with it, but to capitalize the part that follows the particle. The particle is capitalized if the last name with the particle is used by itself.
Correct: Ludwig van Beethoven
Correct: Cornelia ten Boom (First name being used)
Correct: Miss Ten Boom (First name not used)
See Names Not Capitalized for certain names which are not capitalized.