OK, rather than me walk you through building an append query step by step, use the help in access. Type in "Append" and select "Create an append query". I assume you will be working from a form, in which case you don't need the delete query.
When you design the append query, go to the Criteria block under the primary key field and right click and select Build. Find your form and double click on the primary key field to add it to the workspace. Click OK.
This way, when you run the query from your form, it will only append the current record. (Your destination table should have a number primary key, but not autonumber.)
I don't use "macros", but I assume from your post that you do. Make one that will run the query and then delete the current record from the form.
I would use code behind a button something like this:
DoCmd.OpenQuery "MyAppendQuery"
DoCmd.RunCommand acCmdDeleteRecord