desu, iru and aru

This would be a good place to leave the "action verb" endings and explain the "to be" verbs desu, iru and aru.
Desu is added to the end of statements to make them polite, including ones that end in plain verb forms or their conjugations. Do not add it to verbs that are already in a polite form, like something from the masu group.
After nouns and adjectives, desu acts like English "be verbs" (am, are, is, etc.) and states that something (a noun) is something (a noun or adjective):

• Kare wa Tanaka-san desu. (He is Mr. Tanaka.)
• Carol wa nijuu go sai desu. (Carol is 25 years old.)
• Bob wa byouki desu. (Bob's sick.)
• Ashita wa ame desu. (Tomorrow it will rain. [The weather forecast for tomorrow is rain.])
• Sono gakkou wa furui desu. (That school is old.)

The plain form of desu is da, which is used by kids and adults in familiar settings:

• Mite! Hikouki da! (Look! An airplaine!)
• Iya da. (No. [I don't want to...])

I should point out here that the above sentences do not need desu or da to be complete or grammatically correct. In fact, you will often hear them with neither. Desu or da are added to "finalize" the statement in some cases, with desu being the one to choose when the setting calls for polite speech.
Iru and aru mean "to be (in a certain place)" or "to exist." Generally speaking, iru is used for people and animals, and aru for everything else:

• Tom wa iru? (Is Tom here / there?)
• Hai, Tom wa iru yo. (Yes, Tom's here.)
• Kabe ni kumo ga iru. (There's a spider on the wall.)
• Jisho wa tsukue no ue ni aru. (The dictionary is on the desk.)
• Kouen ni ookina ki ga aru. (There's a big tree in the park.)

You can make these polite by converting them to their Base 2 form and adding masu. Iru is an ichidan verb, and aru is a yodan, so be sure to convert them accordingly:

• Tom wa imasu ka? (Is Tom there?)
• Kouen ni ookina ki ga arimasu. (There's a big tree in the park.)

The plain negative forms of these are inai and nai :

• Sumimasen, ima Tom wa inai. (Sorry, Tom's not here now.)
• Jisho ga nai. (I don't have a dictionary.)

And the polite negative forms would use masen, which was introduced in Lesson 4:

• Sumimasen ga, ima Tom wa imasen. (Sorry, but Tom's not here now.)
• Jisho ga arimasen. (I don't have a dictionary.)

The plain past of these are ita and atta, which should only be used in very familiar settings:

• Kinou Tom wa ita. (Yesterday Tom was here.)
• Koko ni ookina ki ga atta. (There was a big tree here.)

The polite past forms are imashita and arimashita :

• Kinou Tom wa imashita. (Yesterday Tom was here.)
• Koko ni ookina ki ga arimashita. (There was a big tree here.)

For plain past negative use inakatta and nakatta :

• Kinou Tom wa inakatta. (Yesterday Tom was not here.)
• Koko ni ki ga nakatta. (There was not a tree here.)

And for polite past negative use masen deshita :

• Kinou Tom wa imasen deshita. (Yesterday Tom was not here.)
• Koko ni ki ga arimasen deshita. (There was not a tree here.)

Now let's get back to desu. Its plain negative form is dewa nai or ja nai :

• Kanojo wa juuhassai dewa nai. (She's not 18.)

And the polite negative is dewa arimasen :

• Iie, kare wa haisha dewa arimasen. (No, he's not a dentist.)

The plain past, polite past, plain past negative, and polite past negative forms are datta, deshita, dewa nakatta, and dewa arimasen deshita, respectively.
There is another form of desu that I've been asked about: de aru. This is one that is rarely used these days. You really don't need to concern yourself with it at all unless you decide to study Japanese literature. The only time you will hear it is on historical dramas or documentary programs. If you are really interested in the technical background, here it is: Among the several roles of de, one is "as," as in being in a certain position, state or condition. Connected with aru it means "to exist as...." So, if you were to say John wa gakusei de aru, you're technically saying "John presently exists as a student" (John is a student). Again, it is rarely used these days in daily communication. Use desu instead.¹
Have I mentioned how "grammatically loose" Japanese is? Well, it is, and you will run into lots of strange constructions which cannot be explained in English simply because they do not exist in English. With desu, there is one way it is often used which will throw the student who is still trying to "think out in English" everything heard in Japanese. This is when it is used after the object. A good example would be:

A: O-tousan wa? (Where's Dad?)
B: Shigoto desu. (He's at work.)

B could even answer o-tousan wa shigoto desu, which, to the mind of the student of Japanese, could mean "Dad is a job," but it doesn't. This is the "wild card" nature of desu.
I realize that making sense out of this will take some time, but Japanese allows much more "vagueness" than English does. In the example given above, desu is simply added behind the minimum required answer as a polite formality, and has no other value as a grammatical component. The seasoned listener will recognize this and not expect desu to mean anything more.

Word Check

ame: rain
gakkou: school
furui: old
hikouki: airplane
iya: disagreeable; unpleasant; No! ²
kabe: wall
kumo: spider
tsukue: desk
ue: the top (of something)
ookina: big
ki: tree
ima: now
jisho: dictionary
haisha: dentist

Notes

1. Most native speakers do not voice the u on the end of masu or desu. If you want to sound like most natives, pronounce them "moss" and "dess." You will, however, occasionally hear a few speakers voice the final su, making them sound something like mah-su and deh-su, with just a very short su. You can imitate the version you like.
2. Iya da! is used as a simple reply to reject something, and is especially used by children.