思う is translated as to think in English. It's used to express personal feelings, opinions, beliefs, or judgments. Here are some simple sentences showing different ways 思う can be used. Note that 思う is used with the particle と in front of it.
思う can also be used to express a decision that you've made.
Note that in these sentences, と 思う translates to something along the lines of I've decided or I intend, indicating that the speaker has made up their mind about the action. It can, however, still have an element of uncertainty, as decisions can change. It's a bit softer or more indirect than more definitive phrases using つもり.