If you’re asking how to get an installable version, I can’t tell you because I always get the CD. Call Adobe Customer Service for advice.
If you have an installer that you downloaded from before, then you should be ok, as long as you have both the current version’s key and the key for the version you upgraded from–an upgrade install requires proof of a previous version, somehow, either by seeing it already installed, or by you putting in the CD and/or entering in the serial of the previous version, depending what version you are trying to install as an upgrade.
Of course, your license (at least for the newer versions, not sure how far back it goes) lets you activate PS on up to two computers that you, yourself, use, as long as you don’t use it on both at the same time…a work computer and a home computer, for example, so you can take your work home.
As far as moving the license, or Activation, from one computer to another, install it on the new computer, to make sure that it will work, then go to the old computer, and use the Deactivate option in the Photoshop menu, maybe the Help menu, then go to the new computer and choose Activate option, maybe again the Help menu or just a nag screen when you start up each day, and follow the steps. The Adobe servers keep track of how many active activations you have and limit that to two per serial number.