Zoe,

         You will need some external media whether an SD card or a USB jump drive.  Whatever can be plugged in to both computers.

Here are the steps, presuming IE 11 on both sides:

On the "old computer side":

1. Open IE 11, File Menu, Import and Export Option.
2. In Import/Export Settings dialog select the "Export to a file" radio button, then hit the Next button at the bottom of the dialog.
3. The "What would you like to export?" step comes next.  Check whichever of the checkboxes you wish.  Favorites are, of course, one of the checkboxes.  Hit the Next button at the bottom of the dialog.
4. The next step asks you where you'd like to export from.  I never touch this as it uses the default location for favorites to export from.  Hit the Next button.
5. The next step asks where you want to save the exported bookmarks.  The default will be your documents folder in a file called bookmark.html.  If you wish to browse for another location and/or specify a different file name hit the Browse button and do so.  I generally go with the default and hit the Export button on the bottom of this dialog.
6. The Favorites will Export (unless something goes wrong) and you'll be presented with another dialog with the Finish button. Hit it.
7. Copy or cut the bookmark.html file from your documents folder and save it on your external media.

On the "new computer" side, insert the external media you've copied the bookmarks.html file on to in the new computer.

1. Open IE11, File Menu, Import and Export Option.
2. In Import/Export Settings dialog select the "Import from a file" radio button, then hit the Next button at the bottom of the dialog.
3. The next step asks what you'd like to import.  Presuming you're only doing Favorites check the Favorites checkbox.  Hit the Next button.
4. The next dialog asks where you'd like to import the Favorites from.  Here you will hit the browse button and then navigate to the external media where your bookmark.html is located, select it, then hit the Open button.  This will place the full path to that file in the dialog text box so you can now hit the Next button.
5. The next step asks you where you'd like to import to.  I never touch this as it uses the default location for favorites.  Hit the Import button.
6. The final dialog should tell you that you've successfully imported and there is a Finish button at the bottom of the dialog.  Hit this.
7. You're done, and should have your favorites in IE on your new machine.

Brian