How do I sort tasks manually on iPhone and iPad?

Manual order is a sort like any other, and reordering happens in batch editing:

1. Open the sort menu on the sort bar above your tasks and choose Manually.
2. Tap Batch Editing at the trailing end of that bar.
3. Touch and hold a task until it lifts, drag it to its new place, and let go. Select several tasks first and drag any one of them to move them together.
4. Tap Batch Editing again when you are done.

If a dragged task jumps back to where it was, the list is not sorted Manually or batch editing is off; reordering needs both. Outside batch editing, touching and holding a task opens its menu when you hold still, and dragging it moves just that task to another list, a tag, or a date without changing its place in the order.

In a list with sections, dropping a task on a section's title, or among that section's tasks, moves it into the section with any sort, inside or outside batch editing. Each section's tasks follow the manual order within that section, and the sections stay in the order you give them.

Each list remembers its own sort and its own manual order. Manual order in the Focus Lists (Today, Scheduled, Starred, All) syncs only with iCloud. A project or checklist keeps a separate order for its sub-tasks: open it and choose Manually from its own sort menu.

See Sorting Manually and Batch Editing.