Intention

In Japanese, intention and will is often shown in a subtle manner, and direct words are often seen as too strong. 

Tsumori

The noun tsumori means "intention", so the sentence ending tsumori desu after the plain form of the verb can usually be translated as "intend to" or "mean to do". Tsumori has a nuance of being a little bit more uncertain or in the future than -you to omou.

それは問題ですね。どうするつもりですか。
Sore wa mondai desu ne. Dou suru tsumori desu ka.
That's a problem, isn't it? What do you intend to do?

どんな車を買うつもりですか。
Donna kuruma o kau tsumori desu ka.
What kind of car do you intend to buy?

-you to omou

Using the -you form of a verb together with "to omou" will indicate that you are intending to do something.

食べようとおもう。
tabeyou to omou
I am going to eat

飲もうとおもう。
nomou to omou
I am going to drink. 

東京に行こうとおもう。
Tokyou ni ikou to omou
I will go to Tokyo.

Softer Ways of Expressing Intent

It is often said that the longer and more complex Japanese sentences are, the politer and softer they sound. It's not a rule, but actually is pretty close to the truth. Here are some examples of sentences that sound a bit softer than the ones above.

映画を見に行こうかなあと思っています。
eiga o mi ni ikou kana to omotte imasu.
I am thinking of going to see a movie.

映画を見ようかなあと思っています。
eiga o miyou kana to omotte imasu.
I am thinking of going to see a movie.

ご飯を作ろうかと思って‥
gohan o tsukurou ka omotte...
I thought I'd make some food...

買い物に行こうかと思うんですが。
kaimono ni ikou ka to omou n desu ga.
I am thinking of going for some shopping, or so.