I am not an expert, so maybe someone else will come on and give more details.
If you are asking just about Golden Skate, you do not have to do anything. You can log on from any computer and with any ISP, and this will not affect your account in any way. You do not need to re-register or anything.
If you mean in general, assuming that you do not want to create a network which includes both of your computers, you should make copies of all the files that you want to save. If you have a CD writer, that's best. You can also save files to floppy discs, but you might need a lot of them, like maybe hundreds if you want to save a lot of stuff, especially pictures, etc.
For programs, the easiest thing is if you kept the original discs -- you can just reload them onto your new computer. (Even better, if the new computer comes with all of your favorite programs already loaded.)
Merry Christmas!
Mathman