You can't just copy/paste the files. It won't work that way. You'll need to buy some imaging software. One software that I know tell you exactly what you're doing and it works great is called "Acronis True Image" (www.acronis.com). Get the home edition one; works just fine.
Basically how this will work is you install the 250GB drive as a second drive (the 'slave' drive). Install the Acronis software on your old ? gb drive(you should mention how many gb your computer). There's an option in the software to "clone" your harddrive. Once you've cloned it to your new 250gb drive, you can swap it back around so the new drive is now the 'master' and the old one is the 'slave' (or remove the old one completely). Now when you boot up, your system will have everything like it was but all on the new drive.
If you're unsure how to make a drive a 'master' and/or 'slave', there should be some instructions that came with your new drive on the jumper settings. You can also google "adding second harddrive" or something similar and find plenty of webpages showing you how to do it.