Minimising the Turn Structure
There are many things you can do, to minimise your turn structure.
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. The turn must still feel sufficient, however.
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 this 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 was 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.
Constantly look for ways to squash your turn, or parts thereof.
The giant menu
For longer-term strategy games (and very light games), I prefer to just take one complex, impactful action. This is how I design most of my games these days.
However, some games require multi-action turns. If a player takes more than one action in a turn, try to put all the possible actions into one menu. "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".
A player 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.
This 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. You can use the abilities of your people and camps. You can play an event card, or use special actions. 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.
There may also be a maintenance step in the turn, such as income or drawing a card. Everything else goes in the giant menu.
The giant menu reduces rules complexity. You might wonder how putting all the usual rules into one menu makes it less complex. The answer is that the structure of the game is simpler. Your turn is basically "draw a card and then choose one thing from this giant menu." The player can understand the game structure, even if they don't know what each thing on the menu does.
I then try to reduce the complexity of each thing on the menu.
All-player & simultaneous actions
Move things to the other players' turns. If there's a maintenance or scoring 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.