There are several ways to do this.  You can use the Import/Export option within the Internet Explorer browser or you can copy the Favorites items stored on the local computer to a different location.

You can export the Internet Favorites to an external file. Save them to a location and import them into another computer, or share them with a colleague.  Depending upon the version of Internet Explorer you are running, the steps should be similar.

-Open Internet Explorer
-From the menu bar, select File > Import/Export
-Select the option to Export to a file, then click on Next
-Click on the Favorites box, then click on Next
-Select the folder that you want to export your favorites from. Click Next
-Identify the location to save the file to. Use the Browse button to navigate to where you want to store this file. You'll need to know this when you want to import the file into the next machine, or to share it with your colleague(s). - Click on Export 
When you want to import the file into the new machine, select the option to Import the file, and follow the system prompts.

Instead of exporting the file, you can copy the links directly from your computer.
-Click on Start > Run > in the Open space, type 'favorites' then click OK
-The Internet Favorites items will appear, click on Edit in the menu bar, then click on Select All. The items in the folder will be selected.
-Click on Edit in the menu bar, then click on Copy
-Navigate to a place where you would like to store these items for future use (i.e., My Documents).  Once there, create a folder to place these items in (i.e., Favorites).
-Open the newly created folder (i.e., Favorites), click on the Edit option in the menu bar, then click on Paste.
-This folder will now contain direct links to your internet favorites. You can paste these items in the same location on the new computer.