Consider taking a slow, leisurely pace with them.
This will keep you from inadvertently exploding their head by infodumping 3 years worth of squiddy knowledge in a condensed time span. Of course, don't treat them like a fool but like someone who's entirely new to this... this... inky madness—which they are as you pointed out. They're a new student, it's their first week of class, and they're learning a new subject they've heard about but never had direct exposure to until now.
Consider starting with the basic stuff: generic terminology, background, slip in a single specific term once in a while with a brief definition while letting them know you'll dive deeper into it later—go full on tutorial mode on them if you must. All the while encourage them to explore things on their own and allow them to ask any questions. Even over things that seems random or innocuous to you, because this is a whole new thing for them, such as if they ask "Why is a there are there cats here when everyone is sea people?!" or "Whoa! Who's the cute chic—EWW—why'd she jump in the sewer?! Can I foll—okay let's go!" you give them a brief answer, wait if they want to know more, and encourage them to explore and ask more questions along the way.
Your results will vary as that's how I often teach some people (anything): give the general info and/or basic demonstration, encourage exploration, demonstrate and answer questions as needed, repeat. And occasional directed nudging helps too.
And if you think your teaching sessions become too aimless or not going the way you want, consider having three concepts/lessons already planned ahead of time. Start them off from there or lead them to it when you both play. For example, teaching your friend about the ins and outs of super jumping, beakons, and abilities: stealth jump, quick super jump, and drop roller either right off the bat or during a private lobby as you introduce them to the different modes. This can serve not only to slowly prep them for competitive (if they're in to it) but is also good general level knowledge for whenever they play on their own.
Let me know if I need to clarify anything. =)