To receive (paste in usual terminology) data from the clipboard, you should create a wxDataObject derived class which supports the data formats you need and pass it as argument to wxClipboard::GetData. If it returns false, no data in (any of) the supported format(s) is available. If it returns true, the data has been successfully transferred to wxDataObject.
For drag and drop case, the wxDropTarget::OnData
virtual function will be called when a data object is dropped, from which the
data itself may be requested by calling
wxDropTarget::GetData method which fills
the data object.