Here are two simple ways of moving files with pros and cons to each method:

1. Using Explorer

• Log in to your site using Internet Explorer
• Go to the source library and from the ribbon click Open with Explorer
• Open a new Window and go to the destination library and click Open with Explorer
• Return to the window with the source library and select the files to be moved and cut using Ctrl + c
• Paste the files into the destination library

Pros:

• Easy and quick to use
• No additional permissions required
• Great for small number of files

Cons:

• Can only done on a PC and using IE
• Version history is lost
• Not practical for moving large quantities of files

2. Using Content and Structure

• Log in to SharePoint
• In Site Settings go to Content and Structure (under Site Administration)
• Use the left navigation to find the site and library holding the files that need moving
• In the right panel, select the files that need moving by checking the boxes to the left of each file (or check all files)
• In the menu in the left panel select Move under Actions
• In the pop-up that appears, navigate to the 

Pros:

• Version history comes with the files
• Can be started and runs in the background
• Great for large quantities of files

Cons:

• Takes a a bit longer than cut and paste
• High permissions required to do this
• Source and destination libraries must have matching columns