First off Duane, your DATA is safe. Your programs, well not so much, unless you have the installation disks, or files.
The first thing you want to do is install this hard drive as a second drive inside your computer. This way you're not fooling around with USB cables. Just remember, power off, plug out of the computer, and keep it as antistatic as possible. Just plug in the Serial ATA cable, and fasten in the drive.
When you boot up your computer, Windows will see it and give it a drive letter. What the letter is doesn't really matter, unless you're planning on keeping it in your system. It's at this time a good File Manager would come in handy. I use EF Commander (http://www.efsoftware.com/cw/e.htm), but it's up to you.
You just want to Move, or Copy the contents of the directory Documents, from your old hard drive to your new C:\ drive Documents directory. It may take a while, but in that one move all your documents, music, videos, everything will be conveniently moved to the new drive.
As for your programs, you're going to have to reinstall them one, by one. As you reinstall them, open them, and upgrade them. If you had any data for these programs anywhere else on your old drive other than the Documents directory, you can copy it over once they are reinstalled. If you can't find the installation file, or disk for your program, contact them. Send them an email, and tell them what happened. They will have your info on file, and will in most cases send you a link to download a fresh copy of the software.
Lastly, and I can't stress this enough, get yourself a big external hard drive, and back up often. That way, you will never have to go through this again. I hope this helped.