When the DHL Versenden / Shipping module has been configured correctly, no additional shipping method for DHL is visible the checkout. This is normal.
The module does not create new shipping methods but instead uses the existing ones in Magento. Activate the shipping methods that should be processed via DHL in the box "Shipping methods for DHL Versenden / Shipping". The shipping costs need to be configured directly in those shipping methods.
The purpose of the DHL module is to transmit the existing shipments to DHL and download shipping labels which can then be printed. The shipping rates are not calculated by the DHL module.
Please also read the information in this article.