How to add text fields to products on my Shopify store editor?

You may either use an app to collect customization information for products or edit your theme code to do the same. Here are some good apps that allow the merchant to collect customization requests from the customer - Infinite Options, Product Options and Customizer, Customify. If you prefer, you can get a Shopify developer to edit your theme code. Also, you can add order notes. Keep in mind that order notes relate to the entire cart, not to specific products.