たいと思う - Usually used to soften your desire to do something, especially when announcing a course of action that your audience has little control over (喫煙の危険について話したいと思います。I think I'd like to speak about the dangers of smoking.)
ましょう - Volitional, offer of help or invitation to participate. Usually formed as a question (喫煙の危険について話しましょうか。Shall I/we speak about the dangers of smoking?)
しようと思う - A course of action decided in the moment. 思っている is something you've wanted to do for a while. (来年、日本に留学しようと思います。東京に行こうと思っています。I think I'll study abroad in Japan next year. I've been meaning to go to Tokyo.)
しようとする - To make an attempt, but success isn't guaranteed. (今日から毎日三十分散歩しようとします。Starting today, I'll try to take a 30-minute walk everyday.)
するところ - To be about to do something, usually a situation that is interrupted.( ああ、ごめん。晩ご飯をたべるところだから、ね。Oh, sorry. I've just sat down for dinner so, y'know?)
つもり - To intend to do. The plan may not have come together, but you want to. (十二月に日本語能力試験を受けるつもりです。I intend to take the JLPT in December.)
する予定がある - To have a plan which was already arranged. (来週の金曜日に愛媛にいる友達に遊びに行く予定あります。I have plans to visit friends in Ehime next Friday.)
する気がある - To have an interest in doing. (兄が空手部に入って以来、弟は空手をする気がありそうです。Ever since my older brother joined the Karate Club, my younger brother seems to have an interest in doing it.)
ことにする - To decide to do something. (彼女が何かをすることしたら、必ずする。Once she's decided to do something, she'll do it for sure.)
まいとする - Try not to. (腹を立ているのに、見せるまいとしたほうがいい。Although you're angry, try not to show it.)
まいと思う - Think no one would~. (誰もわかるまいと思った。I thought no one would find out.)
