There are two options to move items in sitecore from one database to another database - Publish and Tranfer. This post explains how to move items using publish and transfer options in Sitecore.
Publishing an item in Sitecore
Select the item which you want to publish. And select the publish item option as shown in the below screenshot.
Select Publishing type, Publishing languages, publishing targets and then click publish
Transfering an item in Sitecore from one database to another database
Select the item which you want to transfer. Right click and select insert->Copying->Transfer.
A dialog box will appear to select the source item to be transferred. Select the item and click Next button.
At the top select the target database to which you want to move, and then select the destination folder to which you want the item to be moved. Select web database to transfer the item to web database.
Click next button. You can include the sub items by checking the ‘Include subitems’ Then click transfer