Saying what you think (と思います), quoting (と言います), and confirming with でしょう.
Plain-form clause + と 思います = “I think that …”.
あした あめが ふると おもいます。
I think it will rain tomorrow.
The content of your thought is a plain-form clause marked by と before 思います. Use this for opinions and guesses.
と marks a quote before 言います. Direct quotes use 「」.
たなかさんは 「あした やすみます」と いいました。
Mr Tanaka said, “I'll take tomorrow off.”
と quotes speech or thought before 言います. A direct quote keeps the original wording in 「」; an indirect quote uses the plain form before と.
でしょう = a guess (“probably”) or, with rising tone, “…right?”.
あした はれるでしょう。
It will probably be sunny tomorrow.
でしょう expresses probability. Said with rising intonation (でしょう？) it seeks the listener's agreement: “…isn't it?”.