Learn Spanish (Latin America): Yo tengo un carro.

In Spanish, nouns have a gender. The word for car, carro, is masculine (you can usually tell because it ends in an "o"). We use the article un for masculine nouns and una for feminine nouns to say "a" or "an".

I learned that the number "one" is uno. Why did it change to un?

When uno is placed right before a masculine singular noun like carro, it drops the "o" and becomes un. Because of this, un carro can mean both "a car" and "one car" depending on the context.

Do I always have to include the word yo?

No! In Spanish, the verb tengo (have) only ever goes with yo, so it already means "I have". You can just say Tengo un carro. People usually include yo only when they want to add emphasis to the sentence.

I've also seen the word coche used for "car". What is the difference?

They mean the exact same thing! carro is the most widely used word for "car" in Latin America, while coche is the preferred word in Spain.