To think
With normal sentence + と思う = "is what I think"
綺麗だと思う。 I think it's pretty.
Intention to (...), thinking about doing (...)
When with the volitional form (〜oう), shows that you have an intention to do something.
行こうと思います。 I think I'll go.
Sometimes abbreviated, removing the actual 思う. Has a very spontaneous vibe to it.
靴を履こっと I think I'll wear shoes!
買おうと！ I think I'll buy it!
Combined with 〜ている, denotes that it's an ongoing process. You haven't fully made up your mind yet.
北海道へ行こうと思っています。 Im thinking about going to Hokkaido
Don't confuse this with ように + 思う