Assigning a task
Open the project and tap Task on Project Home. The List of Tasks opens with every task on the project.

List of Tasks, with the Dashboard, Planning and status tabs across the top. The tabs across the top move between views: Dashboard for the summary, Planning for scheduling, and All Task, Not Started, In Progress, Delayed and Completed for the task list at each stage.
Delayed is the one worth checking daily. It surfaces work that has passed its date without being completed, so it is visible without anyone having to raise it.
Use the add button at the bottom right of the list to create a task, then assign it to a team member and give it a date so it appears in the right tab.
Task status feeds the Project Progress and Filtered By Status figures on the project Dashboard, so keeping tasks current is what makes that dashboard mean anything.