OP - the battery wanring light just means the charge is low, doesn't necessarily mean the battery is knackered. Do yo do a lot of short runs?
If so take it for a good long run (at least 1 hour, main roads) and see if that helps.
If you do need to change the battery, there's no such thing as an 'OE' battery, just any quality one will do.
But yes, just connect your positive charger clip (any old crappy charger will do) onto the red terminal under the bonnet, it is just an extension of the main positive connection to the battery. Find a good bit of clean metal (engine mounts?) to put your negative charger clip.
Their is a small ground stud on the inner wing near the positive terminal, but it is quite small, better to grab a big chunk of engine.
I have a CTEK 3600 which I use for my other car via cig lighter socket....
Our Ciggy sockets are isolated until the ignition is ON, so you couldn't charge via them. (as are most cars these days to stop kids burning themselves!)
Bit of an odd way to do it, ok for conditioning though, but not charging from flat as the ciggy lighter fuse would blow!!