When expressing one's thought, feelings, opinions, ideas and guesses, "~ to omou (I think that ~)" is frequently used. The particle "to" indicates that the preceding sentence or words are a quotation.
Since "~ to omou" always refers to the speaker's thoughts, "watashi wa" is normally omitted.
Ashita ame ga furu to omoimasu.
I think it will rain tomorrow.
Kono kuruma wa takai to omou.
I think this car is expensive.
Kare wa furansu-jin da to omou.
I think he is French.
Kono kangae o dou omoimasu ka.
What do you think about this idea?
Totemo ii to omoimasu.
I think it is very good.
If the content of the quoted clause expresses one's intention or speculation about a future event or state, a volitional form of a verb is used preceding "~ to omou." To express a thought other than one's volition or opinion toward the future, a plain form of a verb or adjective is used preceding "~ to omou" as shown in the examples above.
Oyogi ni ikou to omou.
I think I'm going to swim.
Ryokou ni tsuite kakou to omou.
I think I will write about my trip.
To express a thought or idea you have at the time of your statement, "~ to omotte iru (I am thinking that ~)" is used rather than "~ to omou."
Haha ni denwa o shiyou to omotte imasu.
I'm thinking of calling my mom.
Rainen nihon ni ikou to omotte imasu.
I'm thinking of going to Japan next year.
Atarashii kuruma o kaitai to omotte imasu.
I'm thinking that I want to buy a new car.
When the subject is a third person, "~ to omotte iru" is used exclusively.
Kare wa kono shiai ni kateru to omotte iru.
He thinks he can win this game.
Unlike English, the negation "I don't think" is normally placed within the quoted clause. It is possible to negate "~ to omou" such as "~ to omowanai," however, it expresses stronger doubt, and is close to the English "I doubt that ~."
Maki wa ashita konai to omoimasu.
I don't think Maki is coming tomorrow.
Nihongo wa muzukashikunai to omou.
I don't think Japanese is difficult.