The easy way to upgrade a hard drive is to use software that can clone a drive. This program would also be useful to backup your complete hard drive.
I use is Acronis True Image. There are several other software, including freeware versions, so googling disk cloning, or disk imaging, etc. will give you some options....
Before you begin, you need to install the new hard drive as a second drive. If it is IDE, then set the new drive as slave (SL) or cable select (CS) by changing the jumper position. See
here for a pretty good explanation.
Once that is done, make sure the PC sees the drive during booting. Then follow the software instructions to clone existing drive to new drive. The software will usually format and partition as necessary, so you don't need to do this before hand.