How do you currently back up your files and stuff on your 2008 Macbook?
If using a TimeCapsule, then you can literally turn on the new Macbook Air and follow the directions to restore your stuff from the TimeCapsule. If instead you're using an external drive and TimeMachine, just plug it into the Macbook Air during set up and you can restore your stuff that way.
If you're *not* currently doing backups, you're asking for trouble. Computers get stolen, hard drives die, SSDs can die, etc. $80 to $100 for an external 500GB to 1TB drive is cheap compared to drive recovery services. Pick up an external drive, use it for TimeMachine to move your stuff over, and keep using it for backups going forward.