Expanding on Paul's solution, you only want the records from the following tables, all of which can be queried by entering their table name in the navigator followed by .list, such as vtb_board.list for the first:
1) The vtb_board record.
2) All of the vtb_lane records that match the Board you want to include. Filter on the Board column so you don't get anything extraneous.
3) If a shared board, all of the vtb_board_member records that match the Board you want to include, assuming the sys_ids of user records are identical between source and target instance (if not... you'll have to configure manually in the target instance).
"Add to Update Set" works in general, but if you don't have that feature or have a board with many lanes and don't want to click into each lane record to click the link, you can export the records as XML (in the list view, right-click any column header and select Export > XML) and then import into the target instance. Although this works and preserves sys_ids, it won't show up in Local Update Sets on the target instance if that is something you want. I wish the Add to Update Set feature let us apply its functionality to selected records in a list. 🙂
