To express that you ‘think’ something in Japanese, the common expression
と思（おも）う is regularly used. As you can probably guess, this is just a combination of the particle
と, plus the
う-Verb 思（おも）う.
とおもう can be used after any verb,
い-Adjective,
な-Adjective, or noun, but will require
だ after a noun or
な-Adjective.
-
ごめん、ちょっと遅（おく）れると思（おも）う。
Sorry, I think I'm going to be a little late.
-
その言（い）い方（かた）は酷（ひど）いと思（おも）うよ。
I think the way you said that was harsh.
-
俺（おれ）はあの人（ひと）が綺麗（きれい）だと思（おも）う。
I think that person looks pretty.
-
これはフランス語（ご）だと思（おも）う。
I think this is French.
Although this structure usually requires
だ after nouns and
な-Adjectives, it is often omitted in casual speech.
If you want to express what somebody else is thinking,
と思（おも）っている will be used. This is due to
と思（おも）う having a sense of ‘permanence’, and thus not something that the speaker could know about another person.
と思（おも）っている can also be used to express your own thoughts when they are currently happening.
-
ジェームスは自分（じぶん）が賢（かしこ）いと思（おも）っている。
James thinks he is smart.
-
来年（らいねん）に新（あたら）しいオートバイを買（か）いたいと思（おも）っている。
I am thinking that I want to buy a new motorcycle next year.