[subject] + 想 + [verb] + [object] [subject] + 不想 + [verb]
想 before a verb means "would like to". It is the soft way of wanting something – a wish rather than a demand.
不想, never 没想. A wish is not an event, so 没 has nothing to negate.
想 is a wish; 要 is a decision or a demand. In a shop, 我想要一杯咖啡 is polite and 我要一杯咖啡 is an order being placed. Refusing with 我不要 is blunt; 我不想 is softer.
On its own, 想 means "to think" or "to miss someone".
很 strengthens it; doubling the verb softens it.