A lot of "how to help the GM as a player" advice seems to come down to some amalgam of "take story hooks & don't be selfish when making a character," which is sort of more some basic gaming etiquette than actually taking on a helpful role.
I have been properly GMing my main group for six years now (though I've often assumed a similar role since my childhood, just without a proper ruleset) and am a player at another table with a campaign going on three years now. Knowing what issues I encountered when I GMed, I decided after a bit to take a more active role in the group and hopefully ease some of the inherent stress of running the game.
With that in mind, here are some things I do for my group as a player that are a general help for our GM & the table in general:
Take good notes & share them. I understand different people have different matters of notes & attention, but notetaking is just a basic skill you can bring to a table to the benefit of yourself, your fellow players, and the GM. The more notetakers at the table, the less likely information will fall down the cracks. I'm one of two notetakers in my second group, and between our two different styles it's typically easy to double check an event from real years prior in the campaign. The first ~15 sessions before we started taking proper notes? Lost to time, fuzzy memory, and context-free notebook lines in the single digits per session.
State your Plans. This applies to a lot of things, but basically boils down to "communicate with your GM." Give your GM a heads up if you have a course of action in mind for your next session (like wanting to visit a specific shop to get some new gear, wanting to investigate a haunted house, chasing down a specific lead in a mystery, etc).
Wrangle Your Fellow Players. GMing can be exhausting needing to run the game, manage the social group, and throwing time at prep that can get chucked down the drain. Again, each group & their needs & styles will be different, but you can ease some of this just by being a bit mindful. If scheduling's a problem, take the initiative on sorting out prime session time with everyone. Engage your fellow players openly on their plans heading into future sessions (and remember to State your Plans for the GM so they can focus their time where it will be of the most use). If your group can get a bit rowdy and/or the GM has trouble getting everyone's attention, give them a hand in returning the group to the game.
Provide Information as Necessary. This will entirely differ depending on group and game, but sometimes the GM might need help tracking a bit of information or looking up a rule (or, if you have good notes, looking up an NPC name or similar past encounter the group has had). GMing can be hectic what with managing the entire game beyond the party in many systems. You can respectfully bring up a forgotten mechanic or the text of a rule (especially if the GM asks for it). Importantly, strive to act as an impartial reminder of information and rules if you aim to perform this facet; you are arguing not to better your case, but to ease some load from the GM. A corollary to this that shouldn't need to be said, but sometimes does: strive to understand the game & how you interact with it. For D&D likes, this means "know your abilities & their functions; read your spells." If something's vague or unclear, ask your GM before or outside of game how they understand it (not that they're necessarily correct, but that you'll be on the same page).
Perhaps most importantly though: take an opportunity to GM if you can. A prime opportunity is if a portion of the group will miss a week or the GM is a bit burned out (or can't run due to not having prep time for a period of time), you can volunteer to run a one-shot or short side campaign until everything's settled. GMing may seem spooky at times, but it can easily be a ton of fun once you get into the vibe of it. Even if you don't enjoy it, taking some time to GM for yourself can give you excellent insights on how to be a better player from the other side of the screen.

















