Well, AutoNumber fields in Access start at 1, not 0, but you probably know this.
If you don't mind losing the data, you don't need to delete the table definition or the field. To reset a field of type AutoNumber, delete all the rows in the table. Close the table. Then Compact the database (from the Tools menu). The next record you add to that table will get a 1 in the AutoNumber field.
If you want to keep the data that's in your table, you can Copy the table, then clear out the original table as explained above, and write a query to append all the fields from the copied table into the orignal table. Finally, drop the copied table (that is, delete it).