DM and player with ADHD, here.

I agree with Tsojcanth; DMing can often be easier, because I'm forced to stay focused and engaged as I try to stay one step ahead of the party. However, prepping to DM can be miserable, especially when I'm not on my medication.

Here's my recommendations, based on my experience in both roles:

DO:

• Draw! Draw your character, draw what's happening, draw a map, draw rude pictures. Even for neurotypical folks, this can actually improve focus. (Plus, if you aren't already an artist, you'll learn a new skill!)

• Take notes. I'm horrible at remembering to do this one as a player, but I'm good at it as a DM. Your mileage may vary. I just hate taking notes.

• Fidget...carefully. A fidget cube is small and inexpensive, and if held under the table, it can be very subtle.

• Apologize if you slip up. This also depends on your group, of course, but I've been open with my friends about my ADHD; if I zone out and realize I need information, I always start with "Sorry, I zoned out, what was that?". If I get overexcited and interrupt, I apologize and let the other person finish. Saying sorry goes a long way!

• Volunteer to be useful. This can be anything from figuring out initiative order for all the players and keeping track of it (which has the bonus of being useful if your DM is also scatterbrained-- I can't tell you how many times I've almost missed someone because I spaced out!), to physically getting up and helping to tidy up the pizza boxes. Tell the DM what you're doing and why, just stay in the room.

• Do something else. This really only applies to online games, but I will often find a different task entirely to occupy me while other players are doing things that aren't relevant to me. I'll often crack open The Sims and work on building a house, or some other thing I can easily alt-tab away from. I wouldn't do anything like this locally, because it's incredibly demoralizing as a DM.

• Plan ahead! When it's not your turn in combat, an easy way to keep things moving quickly is to have an idea of what you're going to do before the DM calls on you. Circumstances can change suddenly and disrupt the plan, but it's always useful to have a plan.

DON'T:

• Check your phone. This falls under the "demoralizing to your DM" category. It's not fun to look up mid-narration and realize nobody is listening to you.

• Get up and wander off without warning. You don't have to break the flow every time; you could certainly tell your DM outside of the game "Hey, if I'm not doing anything, I might get up and walk a lap around the house/run up and down the stairs/something so I don't get disruptive," which I would personally be fine with.

• Pull attention to your character when they don't deserve or need it. I would rather have a distracted player than a spotlight hog. The spotlight hog hurts the other players; the visibly distracted player just annoys me.

Final thoughts: I'm a big proponent of medication, which has helped me immensely, but I recognize it isn't for everyone, and, quite frankly, that's not what you asked. Even when medicated, I still have ADHD, and I will always have it. If you harness it, it can be a wonderful boon to your playing and improv skills; the innate randomness and scatteredness of an ADHD brain can be very useful for coming up with unique and interesting plans and ideas.

Everyone deals with their ADHD differently. The advice I've given here is specifically what I've done, myself, but figure out what works for you. The one thing that has never, ever worked for me is just trying harder to do things like a neurotypical would.

Be like Bear Grylls. Improvise. Adapt. Overcome.