I found this really nice book at B&N called Live to Tell the Tale: Combat Tactics for Player Characters and that was the first time I even thought about player improvement. I’m ordering the book soon and it looks promising.
Improving as a DM is nice, but will just leave you with pitfalls down the line when you start to outpace your players or even when your players begin to have a divide in their skill sets and you have to tailor the experience to either the high end and bulldoze the low end of your players who are coasting along or to the low end and bore your high end players. I am new to DMing but when I was a new player in a rather large group there was a definite divide between my fellow new players and I and the experienced players, granted this was 6 years ago with 3.5e and there are a lot more resources now to get into and understand the game mechanics. There’s nothing that comprehensively explains what you can do and I currently have a new player who wants to get into the game more but suffers from analysis paralysis because of the fact that they can do anything in the game and the world will react accordingly. For me, that was like a breath of fresh air that I wasn’t restricted to set choices, but I don’t have a structure I can give right now to help them.
I would really recommend the book Live To Tell The Tale for players who are struggling with that. It goes through basic tactics and combat decision making in a clear and simple way. Its probably a bit old hat for experienced players but it does a lot to try and help players get out of indecision delay. It has general principles but also advice and strategy for each class and how to synergize well as a group in combat. Hopefully by the end combat will feel a lot simpler to figure out from a mechanical perspective and the game can speed up some for you all.
Depending on class spell choice can be a big factor. I'm currently playing a Druid in one group and I try to tailor my spells prepared for what we're going to do. So our campaign has had a lot of water encounters and interactions with a snake cult. If I know we're heading into water I make sure to grab spells like Water Breathing/Water Walk. If we're facing the snakes I grab Protection from Poison. If I know we're sneaking I'll pack Pass Without Trace.
You don't necessarily have to wait all the way to the boss room either (when you won't always have the chance to rest). Look for the clues and foreshadowing your DM is giving you. You'll probably have some idea of what you're facing well before you get there.
Also depending on your DM there might be shenanigans you can pull that give you advantages (literally). Start fires, create distractions, deceive and ambush, use environmental features to your advantage. DM's handle that stuff differently but often they will reward clever and inventive solutions.
Keith Ammann's "Live To Tell The Tale" book could be really helpful for basic party tactics. It goes over thing like setting up combos (for example using guiding bolt or faerie fire to give the rogue advantage on an attack so they get sneak attack damage) and things like party positioning and using terrain (Heavy armor, high hp and damage resistant classes in the front, low AC and low HP in the back)
themonstersknow.com is the link for his blog. The same author has also published a player's version, Live to Tell the Tale. He also has a supplement that discusses the Beast Master subclass that actually makes it playable. You can download it from his blog.
That's why he wrote one for players to survive. It's pretty clever marketing to create your own demand. https://www.amazon.com/Live-Tell-Tale-Characters-Monsters/dp/1982122692
A constant and consistent reminder to your team on each of your turns that shouting something to everyone else is a free action.
Beyond that, it doesn't hurt to have a group chat and throughout the week between sessions, come up with different "combos" to perform. Could be as simple as fluffernutter, or a complex "what if" that involves planning and set-up.
And if that's not enough, grab everyone a copy of this book, don't tell your DM, have a book club, and watch your DM struggle to challenge you.
PHB, watch some live plays to see how other people interact who you may like. But a good book I've not finished but Keith Ammann provides generally good tips.
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But best thing I can recommend as a player is how to yes and your other characters. Obviously you have to do it within reason. You cannot always yes and everything because some times other people have legit terrible ideas. I'll touch back on this in a second. But knowing when to chime in when to let other players have a moment and when to take contorl are things you'll learn over time. But the best advice is learn how to make the DM's job easier, try and follow story leads, be ready when your turn in initiative comes up so you have a plan and keep combat flowing.
Ok so back to not always yes anding. We had a moment in a game last session where we were fighting a powerful boss but in said dungeon every room we would go in had a more powerful enemy one player at the table cast wall of force containing said enemy. This enemy was going to attack us after WoF came down. THe caster wanted to check out the next room and my character (and myself) planted their feet and said no. It didn't make sense we will be attacked and if we got into combat with something else he couldn't concentrate on another spell. And if that failed or 10 minutes passed and we got into combat we would be in trouble dealing with combat from all fronts. To the point my character said if they opened that door my character was backtracking through the dungeon and leaving out the front door.
Apparently, they also have a book for players.