1) Deliberate on other people's turns
2) Whenever you ask what's possible, include a reason you think it's possible
The first one is somewhat obvious, and yet it takes people a bit of time for people to pick it up. Planning your decisions while other people are enacting and resolving theirs speeds everything up, and only rarely will something change so drastically during their turn that you'll need to throw out everything you've just considered and start afresh just as the referee turns to you.
Planning on other people's turns is ubiquitous amongst experienced players, and so most find it too obvious to mention as advice to new players. But I can clearly spot when a new player has not yet internalised this practice (and it is a practice many of them have to learn), and I see no reason to not tell them explicitly that this is a best practice. Also, while I try to avoid one-true-wayism, I think this is another one of those techniques that is a matter of skill and not style, and thus that doing this is always better than not doing this.
Deciding what to do while other people are busy figuring out the results of their decisions is a very simple way to speed up combat and other structured activities without changing the mechanics of the game. The crunchier the system, the handier it is to have 300%+ more time to plan and calculate bonuses and refer to rules before anything is resolved.
The second piece of advice is perhaps less succinct but also worth learning. Similar to the first piece of advice, I think it is a straightforward matter of skill at communicating and not one of style.
It's very common for new players to ask broad, abstract questions of the form "Can I do [X]?". Answering those questions is nearly impossible for a referee to do off-the-cuff because doing so requires synthesising information about the paracosm that they have with information the player has about their character, and the player in this case has not volunteered the relevant information that needs to be synthesised. This phrasing forces a wholly unnecessary back-and-forth where the referee has to uncover the relevant information to synthesise into an answer by asking the player questions until they stumble across the right information.
If you, the player, think something might be possible, it saves the table time to provide that reason upfront. This allows the referee to shift from trying to model all of the possible ways something could be done while at the same time trying to reconcile those models with their imperfect memories of your capabilities to just evaluating your proposition. It's actually faster to list off three possible reasons you think you should be able to try something and get a yes or no answer for each.
Once again, while doing this is something experienced players generally know to do (tho' I still see many of them do it as well), it's something that takes new players a bit to learn. It's often conflated with "learning the system", but I think it's something distinct from that, since one can understand how one's powers work and still fail to provide that information to the referee.
Once again, while doing this is something experienced players generally know to do (tho' I still see many of them do it as well), it's something that takes new players a bit to learn. It's often conflated with "learning the system", but I think it's something distinct from that, since one can understand how one's powers work and still fail to provide that information to the referee.
