The Exchange API offers two login flows for developers, depending on the use case of your application:
If you are building an application which will run autonomously, there is a separate login flow to follow to ensure your account remains secure.
If you are building an application which will be used interactively, then this is the flow for you. This login flow makes use of Betfair's login pages.
Further technical information relating to each login method is available via the API documentation.