If the shipping costs are not calculated, check if a shipping cost has been set for the total weight of the shopping cart.
If the shipping costs are incorrectly calculated, then a shipping cost rule is set incorrectly. Make the exact same order in your shop as a test. Look at the shipping costs. Check in the management interface which setting is applicable and correct it.
If the customer can not choose a shipping method, check if there is a shipping method added for the country of the customer. For example: a customer from Belgium will not be able to select a shipping method if you only ship in the Netherlands. You can add a shipping method "Pickup in the store" for the country "Worldwide". This way customers from every country can place an order.
In this case, there is usually a problem with the settings of the shipping costs, discounts or surcharges.
Avoid complex discount structures, preferably do not add more than 10 discount rules. This prevents that a discount or surcharge unexpectedly will be added to an order.