I am quite confident with opening the hood of my machine, just I know nothing of hard drives.
Make sure you take fundamental precautions such as disconnecting everything from the mains and the phone line, and wearing an electrostatic wrist strap.
Do I plug the new one into this to form a daisy chain?
Yes but there are additional considerations.
The cable should only fit one way round. This matters. The red wire is pin 1.
You need to check there is somewhere inside the computer to put the new drive. You also need to check the new drive comes with any screws and fittings to mount it securely.
The new drive will need a power cable to be connected, as well as the IDE data ribbon cable. Check if you need a power cable splitter and that your computer's power supply can cope. Checking that the ventilation (fans) is adequate is also a concern whenever adding more devices inside a computer.
If you have two drives on the same IDE cable then one must be designated as the master and the other one the slave. There are little tiny jumpers on the drive to set that. A search on Google should find some instructions on what to do.
The configuration of which hard disks and optical drives (CD/DVD) are on which IDE cables and which are masters and slaves has a performance implication. To quote from a web site:
You want the hard drives and CD-ROM drives on different IDE cables, or the slow CD-ROM drive will affect the performance of the hard drive. A typical configuration looks like this:
Primary:
Master: first hard drive
Slave: second hard drive
Secondary:
Master: CD-ROM drive
Slave: CD-R/CD-RW drive
It doesn't seem to matter whether the CD-ROM drive or the CD recorder drive is the master. Having both on the same channel doesn't necessarily impede CD-to-CD copying, though you're still better off writing from the hard drive.
Check if your computer's system board also has SATA (Serial ATA) connections. Most new ones do. If so, you may be better off opting for an hard disk with an SATA interface instead of IDE. Sorry, I don't know the rules regarding whether you can mix and match IDE and SATA devices.
All in all, an external USB hard disk might be a more attractive option for non-experts but AFAIK it won't be as fast to access.
Do a bit of Googling if you need more info.
HTH, John