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This is the important bit. To transfer all of your emails over -- on fast Internet connections -- select all of your email (or click on one and press Ctrl + A), then right click and select Move and then Copy to folder. Be sure to select the correct folder as to avoid confusion, which was created a few steps back.
While you may be more comfortable in moving directly, in this method we simply copy the emails (and we will delete them later), to make sure that if this isn't successful, you can try again and haven't lost all of your messages in the process).
To read more on this gallery, visit the iGeneration column, where you can read more about migrating your email to Hotmail or Gmail.