It's something I've never done before, mostly because DLC was not that abundant during the PS2 era. So how does it work precisely? Am I right in assuming that I need internet connection, the game disc, some form of online currency and an account with this PS Network thing? I've got some games with DLC Content, or at least a game, LEGO Batman 3 and for once I'd like to try my hand at acquiring this stuff. What's the process?
Yes, yes unless you have the game in digital form but if you did you probably wouldn't be asking this, yes, and yes. You can use prepaid PS3 cards, most debit/credit cards, and Paypal. On the PS3 menu, the store is in the column to the left of your online friends list (which is the last on the right). Each game has their own page and you can browse all its DLC from there. There's a search function if you don't want to look around the store. And if you're redeeming a PS3 card or code, as soon as you enter the store there should be an option to put them in at the very bottom of the first menu.
There's also a browser based store if you don't feel like turning on your PS3 to just buy something. https://store.sonyentertainmentnetwork.com/ It's currently down though since Sony's having PSN issues again. You just log into your accountonceit'sbackup and everything will be there. When you purchase a game it gets added to your Download List which you can access via your PS3. It's a pretty easy site to navigate and there's a search bar on it so you can quickly get to the DLC for the game you want to get it for. I use that site all the time.