This article will take you through the steps needed to understand how to setup your Klaviyo and Shopper Approved accounts to work together.
You will need to set up your Klaviyo API keys in Shopper Approved, which is required for the rest of the integration. See this article for a step-by-step guide on how to do that: http://help.shopperapproved.com/en/articles/6133965-klaviyo-getting-your-api-keys
Once you set up the API keys, Shopper Approved will automatically start sending customer review data for any new customers that have their information sent to Shopper Approved upon checkout. See this article for an overview of the different events and the data that is sent, as well as how to use some of the data to create new mailing lists of customers: http://help.shopperapproved.com/en/articles/6142945-klaviyo-shopper-approved-events
With the events that Shopper Approved is sending, you can then create new SMS or email flows in Klaviyo that get the event data for customers and sends messages to them. For example, you can set up a flow to send a full survey link to a customer that checked out from your site. See this article for an overview of how to set up a flow and use the Shopper Approved event data: http://help.shopperapproved.com/en/articles/6153327-klaviyo-triggers-and-data, Then, you can see this article will take you through the steps of looping through the product data for each product the customer is eligible to leave a review for: http://help.shopperapproved.com/en/articles/6153374-klaviyo-looping-through-product-data
Lastly, you might be interested in pulling in your overall Shopper Approved review data to use in emailing campaigns, such as stating how many 5 star reviews you have or informing about your high rated products. The first step to completing this is to set up a new data feed to pull in the review data through the Shopper Approved API. Then, you can use that data via Klaviyo's internal coding language in your email campaigns: http://help.shopperapproved.com/en/articles/6137043-klaviyo-data-feeds-and-shopper-approved-review-data