（よ）うと思う details
Examples
think I'll do — an intention framed as one's current thinking
今年こそ運転免許を取ろうと思ってるんだ。
kotoshi koso unten menkyo o torou to omotteru n da.
This year for sure, I'm thinking of getting my driver's license. casual
週末は部屋の掃除をしようと思います。
shuumatsu wa heya no souji o shiyou to omoimasu.
I think I'll clean my room this weekend. neutral
本日は私どもの研究についてお話ししようと思います。
honjitsu wa watakushidomo no kenkyuu ni tsuite o hanashi shiyou to omoimasu.
Today I would like to speak about our research. formal
Formation
V(よ)うと思う — 行こう／食べよう／しよう＋と思うattaches to volitional
Notes
Related patterns
Similar
Both announce a first-person decision, but ことにした reports it as a done deed while (よ)うと思う keeps it as thinking in progress — ことにした resists backing out, ようと思う invites it.
Both voice first-person volition, but 手伝いましょう performs the decision toward the listener on the spot (an offer or "let's"), while 手伝おうと思う reports a private, still-revisable intention and puts no one on the spot.
Both state first-person intention; (よ)うと思う presents the plan as current thinking, soft and revisable, where つもりだ states it as already settled.
Lookalikes
One kana apart with opposite jobs — 行こうと思う (volitional) states the speaker's intention; 行くと思う (plain form) is conjecture about what will merely happen.