The web browser can be accessed via a URL specific to your organisation, and which should have been provided to you during your TE Training.
Accessing that URL will present the following screen:
Entering your User ID and password for the TE domain controller and click on the Log On button.
You will be presented with the TE Web UI main screen:
Many of the key processes available in the TE Windows GUI are replicated in the Web UI, specifically around TE Approvals and Testing and Reporting.
Some newer functionalities such as Commenting and Following specific Tasks, Transports and SAP Objects is only available via the TE Web UI.