This can be done by:

1/ Selecting the 'catalog' menu in admin and then choosing "product statuses"

2/ Make sure "track inventory" is checked. 

3/ Create a product status called "Out Of Stock" (if it isn't already there)

4/ Set "Out Of Stock" as your default 'out of stock' status.

If a product has 1 unit on hand, and 1 unit is sold, this will automatically change the product status from "in stock" to "out of stock" 

Cheers