Generally, there are two ways that a customer can get an account in your store.
Option 1 - When a customer completes a purchase they get asked: "Would you like to create an account" and if they select "Yes, create my account" an account will be created for them.
Option 2 - You can invite customers that have previously purchased by going into the Customers section in Shopify admin. Find the customer and select Invite. If a customer has never made a purchase, you can also manually create a user account for them.