I am intrigued. What would I need to buy/get in order to learn and then run a game?
At the very basic level you'd need the 7th Sea Player's Guide and the 7th Sea Game Master's Guide.
Although to be honest... you'd be missing out on a WHOLE lot of awesome stuff if you just stopped there, because the game is chock full of mysteries, conspiracies, and plots, and has NPCs with all sorts of secret missions, dreams, and skills. And unfortunately for your pocketbook these are all detailed in the splatbooks that were written for all seven nations (plus the Pirate Nations), and all six Secret Societies. And because of the MASSIVE metaplot of the gameworld... your GM doesn't get most of the details of these big mysteries of the world without having all these books.
Now granted, some GMs would just create their own plot of the world based upon the basic points offered up the GM's Guide... but trust me when I tell you that it'd be
nothing compared to what the fully written metaplot has established. Throw in a whole heaping pile of additional character generation stuff... and you really find you WANT to play the game with all the splatbooks at your disposal.
Best of luck if you do decide to jump in feet-first. It's not going to be cheap, since everything is out of print.