How to set product display/sort order

First level of the configuration of product display order

Go to System->Configuration->Catalog and click frontend on the right panel. Set the Product Listing Sort By select to one of the options comprised of 'best value' which is the same as 'position', 'name' and 'price'.

Second level of the set up

Go to Catalog->Manage Categories and click Display Setting on the right pane. You can configure both Available Product Listing Sort By, which will affect the sort-by options from which the customer can choose on the front-end, and Default Product Listing Sort By, which will be the default option on the front-end page.

Set the Position value to manually tweak the product order

Go to Catalog->Manage Categories and click Category Products on the right pane. On the following page, you can change the position of any product that belongs to to the category.
To improve Magento performance, it's better to search the products that need to be sorted and then change and save the position values for them. Note: This is a very important tip for large data website.