How would I get started?

I would start with going to the Tools section here and getting used to using some of the tools like FF6usME (multi-editor), the Level Editor, Sprite Editor etc. Also reading past posts and using the search feature to find out information on what you are interested in learning is a good way to get a feel for what is what. Eventually, depending on what you want to do, you'll have to get friendly with the hex editor, which will allow you to make changes that the other editors cannot do. Thankfully there's tons of documentation on FFVI, and learning to hex edit while intimidating at first isn't really all that hard to pick up and get the hang of, unless your name is Justin lol. (insider)

It's all about what you want to do though really. You could make a thread for any questions you may have, or a project you have in mind (in the personal projects section) and nice people like me will be happy to help. When I first started messing around with hacking FFVI (with no previous romhacking experience either) I started with simple sprite swaps, then I realized that I needed to change their palettes in the 'events' via hex also, so I asked around and read up and learned how to go about that. Then, once I got familiar with that I was interested in more advanced event editing, so I asked my friend Angelo if he would like to make some nice events for me! LOL, (half kidding) but you get the idea - little by little and getting your hands dirty so to speak. =)

A lot of new romhackers come in thinking what they want to do will be easy, and is actually really difficult and will get scared away and/or lose interest when they find out how it isn't at all as easy as they'd like and thought, so I'd advocate starting with 'simple stuff' and learning what the limitations are on what can be realistically achieved - and if you still wan't to go through the arduous process of learning and applying that knowledge, making mistakes and learning from them, then you'll get there and have fun doing it.

There's some nice tutorials floating around here from basic stuff to advanced stuff, so be sure and check out the resources.

Welcome to the site!

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I should also say that the more advanced romhacking is called 'assembly', or 'ASM' hacking, and is nothing short of programming. This skill is required for doing the complex game mechanic changes, and writing new code for all kinds of cool stuff. I have not learned assembly yet so I'll leave it at that, but there are some on this site who excel in that area, should you get to that. ^_^