Verbs - Conveying Desire

I've been using this particular form for a bit now, but it always helps to make a formal post on here about it. In order to say something like "I want to swim" or "I want to go home", I have to conjugate the verb appropriately. It's very simple - take the verb stem and add たい onto it. That's it.

私は泳ぎたい。
I want to swim.

アリスは家に行きたい。
Alice wants to go home.

In this form I can treat the words as i-adjectives, so they can be further conjugated to convey negative and past tense.

私は泳ぎたくない。
I don't want to swim.

私は泳ぎたかった。
I wanted to swim.

私は泳ぎたくなかった。
I didn't want to swim.

Next is something that Tae Kim refers to as volitional form. This is essentially saying "let's do x", depending on what the verb is.

For ichidan verbs, the rule is to drop the る and add よう. For godan verbs, the rule is to replace the う sound with the お equivalent and add う, which effectively prolongs the お.

Of course, there are the usual exceptions. する becomes しよう and くる becomes こよう.

ゲームをやろう。
Let's play a game.

買い物に行こう。
Let's go shopping.

少し話そうか？
Shall we chat a little?

There's also a polite version of the volitional form, which is even easier. Simply attaching ましょう to the verb stem achieves a polite version of "let's do x."

そのレストランで食べましょう。
Let's eat at that restaurant.

映画を見ましょう。
Let's watch a movie.

英語を勉強しましょうか？
Shall we study English?

Credit goes to Tae Kim's lesson seen here.