Best advice I can give for starters is to go to the HDD manufacturer's website. Almost all of them have detailed guides on how to connect, Partition and Format a new drive.
Since you have IDE drives with one already installed at the end of the cable, your second one should use the middle connector. Plus, of course, you need to plug in one of the 4-pin power connectors. But before mounting you should be looking closely at jumper pin settings and planning the mechanical mounting of the units in your machine.
Most HDD units have a diagram on them that shows how to set its jumpers on the pins. Your existing drive could be done either of two ways. The simplest is it is set as the Master. (Ooops, there's a variation on this theme. A few drives have slightly different settings, depending on whether the Master is the only drive on this cable, or has an associated Slave drive. But many don't have this different option.) The other major option is it is set to "CS" or Cable Select. In this scheme, the Master will be the one at the end of the cable (which it should be for most systems, anyway).
If your old drive is set as Master already, then leave it alone and set the new one as Slave. If the old one is set a Master all alone and there's a different setting for Master with Slave present, set it that way, then make the new one a Slave. If the old one is set to Cable Select, leave it alone and set the new one also to Cable Select.
Now you can go ahead and mount the two units in your case. Maybe you didn't have to remove the old one to see its jumper settings, and the new one just slips in another slot. Depends on how your cable is, but you may be able to get the middle connector to reach the new drive without rearranging. Otherwise, you must take out the old one and arrange them both. Don't forget to put all the screws in (usually 4 per drive) and tighten them modestly - no need to strip them! Then hook up the signal and power cables.
Next comes setting your BIOS to recognize that a new drive has been added. This may not even be necessary, because many BIOS's are set to auto-identify all drives and figure it all out themselves. But if yours does not do that (watch the start-up screen fast messages to see if it detects two drives) you will have to enter the BIOS. To do that you start up your machine from the off state and usually hold down the "Del" key while it displays its first messages. Soon it will pop up a BIOS menu of places to go to set parameters. Go to the first setup choice, where you'll have a place to set drive info. By far the easiest on modern systems is simply to set the second drive to Auto - it will then auto-detect that drive on every boot-up. When exiting the BIOS, don't forget to choose the option to SAVE your new settings and exit.
If the "Del" key does not get you into the BIOS, start up again and watch the screen carefully, usually at the bottom, for a message on which key you really do need to hold down.
Once the BIOS can recognize both your drives, you will need to Partition the new one (be VERY sure you do NOT do this to your old one!!!). When that's done you need to Format it (again, NOT the OLD one!!!). If you are not familiar with these steps, the can be done in some current Windows OS's from the Disk Management tools, or better yet with simple utilities you can download from the disk manufacturer's website before starting.
If you get this far and still can't figure Partitioning and Formatting, post another note in this thread. Or, if it all works out for you, post a relieved cheer!