Reordering Dashboard Widgets
Widgets are read top to bottom, and the top of the dashboard is the part people actually look at. Putting the right widget there is the cheapest improvement you can make to it.
Reorder your widgets
On the dashboard customization page, drag a widget to where you want it and drop it. The new order saves by itself, with nothing to confirm.
Shared widgets move too
A widget an admin shared with you is labelled Managed by admin and its contents are locked, but you can still drag it into whatever position suits you. The admin controls what it shows; you control where it sits. See Sharing a Dashboard Widget.
What to put at the top
Whatever you would be sorry to miss. For most people that is late work, then what is due today. Reference widgets, such as the workflows you start often, belong further down: you go looking for those deliberately, so they do not need to compete for attention.
If your dashboard has grown long enough that ordering matters a lot, that is usually a sign it has too many widgets rather than the wrong order. See Customizing your dashboard.