You can move tasks by dragging and dropping them within lists or between lists.

You can move the task to another board 2 different ways. You can click the quick edit icon on the task face, then click the "Move" icon. (You can also use the "e" shortcut while a task is highlighted or while hovering over a task)

You can also open the task and click "Move" from the task menu.

Or, by changing the list inline: