Karlie here from the Shopify Guru Team! You can totally create coupons with the Shopify platform! Instead of coupons, Shopify calls them discount codes. Discount codes work by setting a condition for the discount, generating the discount from your Shopify admin and then allowing your customers to enter the discount code at the checkout stage so that they can get a percentage or amount off of their purchase! You can generate discount codes for a dollar value discount, a percentage discount, or a free shipping discount.
To create your discount codes, you would want to head into your Shopify Admin and then to 'Discounts', like this. From the Discounts page, you'll want to click 'Create discount'. You can enter your discount code's name in the Discount code text box, for example - if you're wanting to offer a free shipping discount code, you can call your discount code 'FREE SHIPPING.' And then, you'll be able to set the condition or rules that your discount code applies to the order by adjusting the 'Options' setting.
If you would like to check out a detailed step by step guide on how to create your discount codes from your Shopify admin, be sure to give this guide a read through!
Another way that you can offer discounts to your customers is by using an app from the Shopify App Store. There are a couple of apps that I would recommend looking into, be sure to check out Sale Rack which is an app that would allow you to bulk update your pricing to include discounted amounts and would allow you to schedule price updates or sales for your customers. I would also check out Product Discount which you can use to set up discounts by 'Product Brand', 'Type', 'Collection', 'Hand Picked' and 'Store Wide' as well as schedule store wide sales!
I hope this helps, but if you have any further questions - be sure to ask and we would be happy to help!