Minimising the Turn Structure
There are many things you can do, to minimise your turn structure.
Put everything in one menu
All turn options should generally be put into one menu. They should not be a series of different menus of choices. "You may do A or B or C" is much faster than "you may do A or B, then you may do C or not", and offers the player more freedom. For more complex parts of a game, players might pick more than one choice, but it would still be from one menu. Giving each thing a cost works in much the same way, though you'll need to record how much you've paid, which is a significant overhead.
A player also doesn't need to do every action every turn. Instead of having "move", "cast spells", "camp" and "battle" steps that you go through each turn, you put them in a list, and let the player choose any two. These actions can then each be significant, as you're only using them some of the time.
You can carefully calibrate how many actions is sufficient for the player to have a fulfilling turn. You really want this to be two things.
Not only is a single menu faster, it also forces the player to choose between very different things, which is a much more interesting choice. They don't say "well, I don't really want to go anywhere, but it's the movement step, and I get a free move. So, I might as well go, umm, that way."
In Radlands, you can put people onto the table, and you can have them use their abilities. You can use your camps, or use special actions like drawing a card, or playing a special event. However, all these things are in a single step. There is no separate "combat phase". All these things cost an amount of water to activate, and you have three water to spend each turn. Once you've spent your water, you end your turn.
Some tricks
Be careful of giving players options they can do on a turn, but usually don't. These always require thinking, and they can also make it unclear when a player's turn has actually ended.
Another way to simplify your turn structure is to cut your turns up into small bits, and have each bit be a turn. It's better to do half as much on a turn, if it means you wait half as long for your turn.
For simpler games, "rest turns" are fine, wherein you might just draw a new hand of cards, replenish your energy, or the like. This allows you to remove "draw a card each turn" or "gain one energy each turn" from the turn structure, which is often essential for family-weight games.
In Ticket to Ride, a player's turn is either spending cards to build "tracks" on the board, OR taking two new cards. I agree with this structure, especially since the game is fairly light and simple.
Simplify individual actions. It's better to have some short turns, and some long, than all long. Look at the most common actions. Make them simpler. Think about the length of each action. Drawing a card is very quick. Executing a card is slower. Doing something with a cost will take twice as long.
In my adventure game, a player's turn would be to do a movement, and then an action. This wasn't interesting enough. Players would usually just do the same things, and couldn't move faster, at any cost. I thought about adding an action point system. A player would spend perhaps 5 points each turn, and each move and action would have a cost. Making the moves and actions compete for the same action points is interesting. If you did a small move, you could do a big action, etc. The problem is that this requires tracking the action points. Whenever you do an action, you most physically record this, by spending tokens. Also, you need to "recover" these tokens after your turn. In a game built around a simple turn structure, I didn't want this accounting. I thought of maybe having a system where all your choices are in a row. You'd use a move, and then an action to the right of it. If you chose a weak move, all the way at the left, you'd be able to choose any action. If you chose a strong move (which would be over at the right), you'd be limited to a few weak actions. This would be a great system for another game, but this would be an interesting puzzle that took focus away from the rest of the game. In the end, I decided that the player's turn would be to first choose an action, and that action would say, at the bottom "and then move 2 spaces" or "and then move 3 spaces". This is less interesting, but vastly simpler. It did require that I condense movement down to basically just "move X spaces", but it was worth it. If players gained the ability to fly or teleport or something, that could be an exception done some other way.
All-player & simultaneous actions
Move things to the other players' turns. If there's a maintenance step, can everyone do it at once?
Your game may be a normal, turn-based game. However, there are always opportunities for parallelisation.
In my adventure game, there were cards that would replenish your resources. They were boring, but had to be there. Later, I changed them to give all players resources. This meant I could have far less of them in the game. Drawing a card that gave all your opponents a benefit was feelbad, so I made the player who drew it get twice as much.
Forced planning ahead
Do not add effects that force the players to plan out their future moves. The players will respond to this by simply taking 1-5 minutes to do it.
Discarding down to X cards each turn is a chore, and it forces the player to think about the possibilities for each card. They probably won't play all those cards, so it's not that important. However, they'll still take time to think about it.
Other kinds of actions can do the same thing.
In Wingspan, there are birds that move from one habitat to another, when you use them. What habitat should you move them to? Well, that depends on what action you're going to use next. Better plan out your next turn right now, and put this bird in the right place. Personally, I would've omitted these cards, or just removed the choice, and simply made them move to the next habitat.
In Pulsar 2849, on each turn, each player will place two dice. They'll use this to fly spaceships around, build things, and upgrade technology. This is interesting. However, at the start of each round, there's an extensive and convoluted phase where players choose their dice for the round, from a shared pool of rolled dice. Furthermore, players typically plan out their whole round during this phase, before picking dice.
If a player is going to be putting extensive thought into something, it should be their strategy, not a side-quest like discarding cards, or calculating their exact next move.