Once you have setup your groups, origins, or dimensional rules inside of ShipperHQ you then need to assign them to products. This article explains how to synchronize ShipperHQ in Magento 1&2.
Within Magento you would go to
Catalog->ShipperHQ->Synchronize ShipperHQ. If you select this you can then see all the relevant data from ShipperHQ and sync it to Magento.
In Magento 2, the Synchronize menu is under
Stores->Synchronize with ShipperHQ
Please note that values that are assigned to current products will not be deleted automatically, e.g. if you have a shipping group BIKES which you create in ShipperHQ and then delete it will not delete from Magento unless unassigned from all products.
Currently we do not support renaming of attributes in ShipperHQ, this will be seen as a new value.