1. To add an assignee, open the assignee dropdown on a task and hover over the person you want to add. Click the Add button that appears when you hover on the person row.
Tip: You can also cmd/ctrl + click the person who you want to add. If you want to select a range, hold shift and click on the start and end of the range of people you want to add.
2. If you want to reassign a task, meaning the current assignee(s) will be removed, just click the name of the new assignee.