On process details page:
if the task is already assigned, use link button "Reassign"
if the task is not assigned yet, use link button "Assign" to pick the assignee
On task details page you can assign the task using the same buttons "Assign" and "Reassign".
When the task is assigned and you click "Unassign" button, the task becomes available to all other assignment candidates.
You can change task availability (until it's assigned to some user) on task details page. Click on the field "Candidates" and choose users or groups you need.