To be or not to be

To be or not to be, this is the question (Shakespeare). And in Japanese it's a good question. The reason for this is simple - Japanese have two verbs with meaning "to be", ある (aru ) and いる (iru). And in this post I'll try to inspect the difference between them. So let's start.

Usages of this verbs
If you look for a simple explanation, when to use ある and where いる, the answer will be:

いる - for living things. Ex. ねこが います (neko ga imasu) - there is a cat.
ある - for not-living things. Ex. くるまが あります (kuruma ga arimasu) - there is a car.

Simple, right? No so quickly.  If the cat is dead, it will be referred to あります (arimasu). And if the car is moving in the street, it will be referred to as います (imasu). And now you'll say WHAT? WHY?
The rule of います (imasu) and あります (arimasu) goes like this:

いる - for animated things.
ある - for not-animated things.

Examples of usage
And now for the examples. Here the situations we can use these two verbs. 

Statement of being: 
へやに ほんが あります (heya ni hon ga arimas) - there are books in the room.

つくえの うえに ほんが あります (stukue no ue ni hon ga arimasu) - there is a book on the desk.

Possession: 
わたしは ほんが あります (watashi wa hon ga arimas) - I have books.
Note: typically the わたしは (watashi wa) is omitted. 
Something happening:
あしたは おまつりが あります(ashita wa omatsuri ga arimasu) - tomorrow a festival will take place.

Questions and answers

Asking questions:

へやに だれが いますか (heya ni dare ga imaska) - who is in the room?

へやに なにが ありますか (heya ni nani ga arimaska) - what is in the room?

Answering:

へやには だれも いません (heya ni wa dare mo imasen) - There is no one in the room (a person)

へやには なにも いません (heya ni wa nani mo imasen) - There is no one in the room (an animal)

へやには なにも ありません (heya ni wa nani mo arimasen) - There is nothing in the room (a thing)

Yes/No questions:

やまださんが いますか (yamada san ga imaska) - Is Mr. Yamada present?

ほんが あります (honga arimaska) - Is there a book?

Answer:

はい,  やまださんが います (hai, yamada san ga imasu) - Yes, Mr. Yamada is present.

いいえ, やまださんは いません (iie, yamada san wa imasen) - No, Mr. Yamada is not present.

Note: pay attention that in negative answer, が is switched to は.

Note: If the form of the example appears only for あります, it will be the same for います and vice versa.

I hope this post was helpful and clear all the misunderstandings. If you still have questions, you are more the welcome to ask them.