Install SolidWorks on your "new" computer.
Start SolidWorks on your "old" computer --> pull down menu help --> than "transfer license" or in newer version "deactivate license".
Start SolidWorks on your new computer and activate or use 30 day trial (don't activate).
If your using an SEK license (issued by your school) then you wont need to do what Richard says. You can just use the SEK on any student install. Otherwise with any other kind of license you will have to transfer/deactivate it as above.