[subject] + 想 + [verb] + [object] [subject] + 不想 + [verb]
想 before a verb means "would like to" or "want to". It is the softer way of wanting something – a wish rather than a decision.
In this sense the negative is bù xiǎng不想: a wish is a state, not an event, so 不 negates it.
想 is a wish; yāo要 is a decision or an order being placed. In a shop, 我想要一杯咖啡 is a polite request and 我要一杯咖啡 is the plain way to order. When turning something down, 我不想 is softer than 我不要.
想 takes degree words such as hěn很 and tè bié特别; 很 in front makes the wish stronger.
With a noun or a clause after it, 想 means "to miss" or "to think".
Doubled as 想想 or 想一想, it means "think it over".