Can I just change the address field and then it will move the business to the new location? I’m not sure how to do this. Thanks.
No.
If the business is mapped as a way or relation (an outline) then you can delete the business information from the old location and add it to the new location (other than address etc. which has changed). In the (default) iD editor, this might be easiest to do by expanding the “all tags” information underneath the form on the left, swapping the tags to text view and copy-pasting the relevant ones on to the new location
If the business is mapped as a node you can generally drag that node to the new location. If the address is stored on the node it might be a good idea to follow the instructions above for a business mapped as an area instead to preserve a bit of history about what was at that address previously.
If the specific business is some kind of shop then you can also create a new node where the business has been moved and mark the old location as shop=vacant, alongside removing all the business-specific information (name, opening hours, etc. but not addresses and the like) if one can see an unused retail space at the building.
This has the advantage of preserving the history alongside giving others an information that a building has some sort of (unused) retail space now.