Jez,
You can get a sub in your car with your standard head unit - you can either use an amp that uses speaker inputs (rather than rca signal cables), (you can take feeds from your rear speakers) or you can use speaker to RCA connectors that, again, tap into your speaker feeds and leave you with connectors that will plug straight into an amp.
However, both of these methods will give you a diminshed quality result compared to proper high volt line-outs. It also leaves you with a slight switching issue, as your current head unit won't have the ability to switch the amp on via a remote lead. However, this is not insurmountable.
I would also consider fitting some caps to your standard speakers if you're intending on keeping them for a while, as these will filter out the very lowest of lows, make them more efficient, and allow you to drive them harder before the inevitable distortion sets in!
Finally,
amp wiring...
Make sure you connect the Negative wire to the amp last. This is to prevent a spark and is more safe. Trust me i do this stuff everyday
It really doesn't matter which order you connect them up. You will only get a psark if the power cable is connected to the battery, and you definitely should not be connecting it if your power cable is energised.
The last thing you should be doing (after your amp is all connected up) is reconnecting the battery and installing the in-line fuse to your amps' power cable.