Common discount scenarios like provide 20% discount if you have previously placed more than 3 orders.
Pre-requisites / Requirements:
Purchase history can be validated only for a registered/logged-in user
The ONLY way to establish and validate whether he is a first timer or a returning customer is "when he logs in"
Only when he is logged in, we can
retrieve his previous purchase history
if there is a previous purchase, he is a returning customer
If there is no purchase, he is a new, first time customer
As a result, this discount scenario can only be run:
When customer logs in
Only at the checkout
Let's see with an example:
Go to WooCommerce -> Woo Discount Rules.
Click Add New Rule.

The purchase history conditions will be in Rules(optional).
Scenario 1 :
I want to offer a 20% discount for customers if they have previously placed more than 3 orders.

Scenario 2 :
Provide one specific product for free if their number of previous order are more than 10.

Scenario 3 :
Provide 30% discount if the Number of orders placed are more than 3 in the Current month.

Note:
You can also choose your own desired dates from the purchase history selection and provide a discount.
While testing, make sure to have a user account that matches the purchase history conditions.
Discounts will be applied only in checkout upon validating the email id.
Video:
Still, unclear?
Please submit a support request. We are always happy to assist you :)