How do I reopen a closed work order?
Open the closed work order and press Reopen. Type the reason and confirm. The reason is kept in the work order's history.

Only someone with the permission can reopen. By default that is the owner; other roles can get it in Settings › Users, permissions, on the Permissions tab.
An invoiced work order can be reopened only after its invoice is cancelled (How do I close a work order with or without an invoice?).