DeliveryMethod in litium 8

In litium 7 I was using
ModuleECommerce.Instance.DeliveryMethods.Get(deliveryMethodId, Solution.Instance.SystemToken)
to get DeliveryMethod object, as I understand in litium 8, I have Shipment.DeliveryCarrierId, but didn’t found how I can get DeliveryMethod object based on that

Did you check the Litium.Sales API reference?

Both the shipment and the payment have a reference based on an provider identifier, the provider identifier is built from two part, the provider id and the provider option id. To find the correct option for the provider the ShippingProviderService/PaymentProviderService need first to be used to fetch the provider information, in the result of them there is a collection with the options.

The references for the shipment is the Order.ShippingInfo.ShippingOption and for the payment the Payment.PaymentOption.