Adding a search function is the number one standard in designing e-commerce websites. They should all have one as they allow customers to quickly and conveniently locate what they’re looking for. It’s similar to asking an assistant in a supermarket where a particular product is. You may know where the cereals are, but it can be difficult to locate the exact brand amongst the hundereds on offer. The same rule applies to an online shop, browsing through categories can be a long process.
In terms of design, once again Amazon wins out. The bar should be located at the top of the page, above the fold where it can be seen instantly. Use a standard white background for text entry and surrond it in a dark colour to make it stand out. You should also make it as long as possible so that users don’t have their queries cut off. Some search functions suggest words as you’re typing to make the process easier but I think some less experienced users would find this confusing and off-putting.