On the order list page in your Order Management System (OMS) you can search by the customer's last name and pull up their entire order history, or you can go to orders/advanced search and search by first and last name, which might pull more specific results. Also, on the summary page of every customer record, you can see their order history in the "Customer Orders" section. Here, you will see the order totals, and you can click on each order to see it.
If you get no results in these searches or can't click on the orders in the customer record, then you have your OMS set to archive historical orders (often set to archive orders that are older than 1 year old). You will have to first unarchive your orders to see them. (Orders/archive (blue button at the top)).
Once the orders are unarchived, you can go back to the customer record and you will be able to click through to the orders. Also, once they are unarchived, you can search orders by last name at the top of the order list page in your OMS, or, you can search by last and first name in orders/advanced search, and you will get results.
Once you are finished with your research you can re-archive the orders.