What signs can I detect to know if a customer will purchase my product?

If we are talking about online marketing, the most obvious sign probably will be that potential customer returns few times to one product. It means that he/she is interested in it, and probably he/she is comparing Your product to same product in other websites. That's why is very important to use Google Analytics or other data measurement systems.

If potential customer comes to Your shop in person, clear sign that he/she is interested in some product will be the time what he/she spends to research the product, and current time depends on how expensive purchase it's going to be for the customer.