The whole cloud service thing won't be available until the Fall update, which will probably happen some time in November. You could either use a transfer cable (costs extra), or you could use any old flash drive. If you use a flash drive, your Xbox would need to format it, so be sure anything important on it is off, in case your press the wrong button. If you use a transfer cable, you connect that to your old hard drive, then connect it to your Xbox, and then get everything straight off the hard drive.
Flash drives would make it a lot easier, it would just take a little extra time, and cost less money if you already have one.
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