[subject] + (很) + 想 + [verb phrase]
[subject] + 要 + [verb phrase]
[subject] + 要 / 想要 + [noun]
想 and 要 both translate "want", at different strengths. 想 is a wish: "would like to", "feel like". 要 is a want you mean to act on, and is often closer to "going to".
The first is a hope. The second is a plan, maybe with the ticket already bought.
要 takes a noun directly: it's how you order. 想 needs 要 after it to mean "want" a thing; 想 + a person means "miss".
想 takes 很, 非常 or 真 for "really want to". 要 doesn't.
不想 is "don't want to". 不要 before a verb is usually "don't!", an order to someone else. So "I don't want to go" is 不想.
With 我 as the subject, 我不要去 is a flat refusal, "I'm not going!", where 我不想去 states a feeling.