You can offer a great service to your customers and it won’t cost you, besides the development effort (and time = money, I know), anything!
For starters, you might want to read the Integration Guide for hosting providers or large websites.
Secondly, ACME, the protocol used for issuing certificates, is a “client <-> server” kind of set up. On your server(s), you’ll need to run an ACME client, which will communicate with the Let’s Encrypt ACME server.
Which ACME client you’ll require, depends on your specific set up. Perhaps you’re offering cPanel to your customers: in that case it can be as simple as installing the Let’s Encrypt plugin for cPanel, based on AutoSSL.