Adjusting Items order (not using columns)

What is the best way to change the order of a list not using an existing column. I understand the ORDER ASC/DESC sql but have seen other websites that allow a user to use up and down buttons to change a list order. Some WA user interfaces have the same function.

My current method is an order field in a table and to manually change the numbers to achieve the preferred order. Hardly dynamic. What would the sql/php look like to allow up and down buttons to move a row?

I'm thinking the up button subtracts the current order field by 1 and the order value of the field with the previous value adds 1. But don't know how to do this.

Also need some scripting as well

Note: The WA tutorial on order by different columns is not thje solution I'm looking for.

Any pointers?