Task delegation is done from the tasks interface.You just have to select the character to whom you want to delegate the task and then click the "Delegate" button.
To get to the tasks interface, you have two options:
1. By clicking a character, clicking the "Delegate" button, and then, on the task tree, clicking the task you want to delegate.
2. By clicking the button that gives you access to the team interface (it's the button between the "+" and the "Island" button in the main interface). On the panel, click the "Delegate" button and then, on the task tree, click the task you want to delegate.