Half of game design is game design, and the other half is simplification.
Reducing complexity is one of the hardest and most important parts of game design. It's something that needs to be done to almost every game prototype I see.
Your game should be explainable (roughly) on a reminder card (a normal-sized playing card.) I'm feeling generous, so you can use the back too. One side should be the objective and the things you can do on your turn. The other side can be icons and miscellany. Radlands was like this during playtesting.
Most of my games have rules that can be written on a single card. I eventually write a proper rulebook, but during playtesting, that's how simple the rules are.
A properly-simplified game is usually just the core, plus one or two other simple systems that support it.
This might sound excessive, but this is pretty much what I usually tell designers whose games I play. And, it's good advice in those cases. It probably applies to your game too.
First, remove a third of the complexity of your game by removing systems outright.
Take what's left, and halve its complexity.
I wish I could give more detailed advice about removing complexity, but it comes in so many forms. All I can really do is try to convey my attitude regarding its removal, and how much you need to do.
The key to reducing complexity (after you've just removed a whole lot of stuff), is to merge things. Find things that work in similar ways, and make them work in the same way, as part of the same system.
If you play cards, but can also fight, could fighting be a card you play?
I recently played a game where players would select vegetable tiles from a central pool, and place them onto their farm in patterns. Also, the player would start with bonus tokens with special abilities. These tokens could be used each time you completed a column of tiles.
I told the designer to
just make the bonus tokens into tiles, and put them into the central pool. Players can just take and place these tiles like any other vegetable, plus there's a little bonus written on there. Much nicer.
Make things work the same way.
A Feast For Odin has 61 action spaces on the board, for players to choose from. This is an enormous amount, and far too many for most games. However, board complexity is greatly reduced by the fact that almost all the spaces work in just a few ways — largely giving out or converting resources.
I don't worry about complexity too much at the start of my design process. It's towards the end of the process that I apply a "bar". It's not a mathematical equation, but every rule and part of the game must add a certain amount of gameplay, per unit of complexity. This causes me to redesign and reword many things, and cut others. This bar gradually creeps up, and by the end of the design, almost everything is simple, and some things are gone.
You want to go over every single thing with a fine-tooth comb, asking "can I possibly remove this text/icon/concept/rule?" You can usually make something half as complex, but 90% as good.
Get rid of anything that creates an exception to the normal rules, unless you have lots of worthwhile things creating the same exception, then you probably need to just turn it into a rule.
Never add a rule, in order to fix a problem.
This is a well-known piece of advice.
Instead, create components within your existing rules, that fix your problems.
Radlands had an issue that the game would snowball in the winning player's favour, with one player having a group of people in play that would wipe out the opponent's people, and leave them unable to recover. Rather than add rules to deal with this, I added the cards Radiation and Famine, which kill most of the people on the table.
In one of my prototypes, it was common for players to amass too many cards. Rather than create a rule that set a limit, I just added a little ability on a couple of cards, which forces players with very large numbers of cards to discard some of them. After that, players avoided building up too many cards.