I will assume that youre using either XP home or professional but the procedure is similar for any OS.
If you just have the single hard drive in your system at the moment then it will be set up as a single master by the positioning of a "Jumper" at the back of the drive.
The jumpers are small plastic pieces with a metal connector inside that connects two pins together on the hard drive to set it as a single master, a master with a slave or as a slave depending on which pins are shorted out by the postion of the jumper.
What I would do in your position is to remove the existing drive and fit the new drive in its place as a single master.
Install your operating system on it, this is where it differes between XP and the earlier OSs as XP starts and installs from the cd whereas 98 and ME have to be started with a floppy boot disc then installed from the cd.
Once your pc is running properly then add the original drive back alongside the new one, you will need to set the jumpers for a slave on the old one and maybe there may be a different postion on the new one for a single master or a master with a slave.
There is usually a digram on the hard drive itself showing how to position the jumpers.
When you restart the pc the new drive will show as Drive C and the old drive may be E or F depending on how many CD or DVD drives you have but you can easily see which it is when you open My Computer.
To transfer your data from the old drive to the new one just create a new folder on your new drive and open it and then copy and paste whatever you want from the old drive into it.
You can then format the old drive to wipe it clean and you can then remove it or leave it in place as extra storage if desired.
If you remove it then you may have to reset the jumper position again on the new drive.
I hope this explains it fully enough for you, if theres anything that you dont understand or would like clarification on please ask