Go to the Contributions > All Contributions menu item and select the desired contribution by clicking on the edit icon
Perform whatever steps you need to in order to complete the contribution - e.g.; find the item they ordered, put it in a box with an address on it, arrange for shipping, etc.
When you have completed contribution processing, click the 'Mark Complete' checkbox in the top-right corner of the screen
Note: You can go back and update completed contributions even though they look greyed out. Just click on the edit icon for the contribution.
You also have the ability to bulk complete contributions. You can do this by selecting the contributions by clicking the checkbox next to them, then clicking the 'Bulk' dropdown in the top right, and then clicking 'Complete / Processed'.
Note: Marking a contribution as 'Complete' or 'Incomplete' does not affect whether the payment was processed.