There are many ways to create a task card:

from a private chat – this way the person will automatically become a task's assignee;
from a group chat – the task will automatically be assigned to this group;
from Cards Feed;
from Task Board of any group – and the task will automatically be assigned to this group.

You can edit the list of assignees, add attachments, poll, sub-task, checklist, time estimate, due date and members/followers

How will assignees know about the task?
All the assignees and groups you specified will be notified that you have created a new task for them.

The new task will appear in their Inbox and My Tasks or Task Board (if assigned to a group).

Assignees can either Accept or Decline the task