The combination of a verb with the 助動詞（じょどうし） (auxiliary verb) う, or よう, followed by the う - Verb 思（おも）う gives us the common Japanese expression ようと思（おも）う. This expression is often translated as ‘I think I will (A)’, or ‘I shall (A)’. It is also close to the casual expression ‘I’m gonna (A)’.
Remembering that う and よう can have one of three possible meaning in Japanese (as shown in the よう grammar point), ようと思（おも）う is usually only used to express one of those three. That ‘one’ is as follows.
意志（いし） - Expresses intentions (has a similar meaning to ～するつもりだ）

• このゲームはもうあきらめようと思（おも）う。
  I think I will give up with this game.
• 私（わたし）は明日（あした）から電車（くるま）で通（かよ）おうと思（おも）う。
  I think I will commute by train from tomorrow.
• 来月（らいげつ）、バイクを買（か）おうと思（おも）う。
  I think I will buy a bike next year.

This expression is also often used with 思（おも）っている. In these cases, it highlights that the intention of the speaker is something that they regularly think, or have been thinking about for some time.

• 今晩（こんばん）はレストランで美味（おい）しいものを食（た）べようと思（おも）っているけど、ナオミも来（く）る？
  I am thinking of eating something delicious at a restaurant tonight, but Naomi, do you want to come too?

思（おも）っている may also be used when describing the intentions of another person, as discussed in our lesson about と思（おも）う.

• タケル、お前（まえ）は絶対（ぜったい）サチコと別（わか）れようと思（おも）っているでしょう。
  Takeru, you are definitely thinking of breaking up with Sachiko, aren't you?