There has been some good advice. Here a take on a defensive approach that works well for me to beat the extreme AI.
You can try to beat the AI on extreme difficulty by playing defensively and stopping their first 1-2 strong pushes and after that I’ve pretty much always been able to win from my experience by just overwhelming them with siege and a good army composition thanks to a good economy.
A castle where the enemy attacks makes it a lot easier and you can make a defensive tower early if you are in trouble to defend key locations.
Like others said a sold build order is very important. If possible push at least 1-2 deer to have another advantage. On Arabia I never go up to feudal later than with 22 villagers - never have idle time in the TC - always pump out villagers unless you age up or are researching loom or other techs.
Try to wall your base - use the buildings you build anyways also as part of the wall. You can also do smaller walling towards your TC.
If you haven’t yet you can watch some youtube videos from The Viper or Hera or other pros to get an idea how to wall efficiently.
Scout the enemy once he goes feudal to see if he makes a stable or archery ranges. That helps to know what you are up to and you can make some skirms against archers or some spears against his scouts to defend.
If he attacks with a massive feudal archer/skirm army you might need a tower to defend from that push.
I know not everyone agrees but I usually want to have horse collar before I place my first farms since that will delay the reseeding considerably and you can deal with the AI also with taking that tech.
Double bit axe is mandatory anyways the moment you reach feudal age.
For skirms to be effective against archers they need the attack and the defensive upgrade which is somewhat expensive and I usually don’t want to over-invest into the feudal defense if not neccessary so if you can defend with a tower or just the TC and some emergency units thats perfect.
I usually go up to castle age with 18-20 on food and 7 on gold, build 2 stables and research all feudal blacksmith upgrades for the knights + blood lines.
Upon reaching castle age you should be fully walled. I usually build 2 more town centers to boom (sometimes the 3rd is a bit delayed) and I immediately make 6 knights. With those you can either defend from an attack or harass the enemy - don’t waste them. Keep producing some more knights.
If you expect some massive attacks you can delay the TCs and build more army.
Early castle age you can also build a siege workshop to have 1-2 mangonels or some scorpions to defend against an early attack from behind the walls.
This is usually enough to keep the AI away for a bit and to have some time to boom.
Also collect stone in castle age to make a castle where the enemy usually attacks you and prepare some army for a potentially strong castle age push with rams, archers, pikes, skirms most of the time.
This push can be quite overwhelming if you are not prepared so mass some knights or other units and some mangonels to deal with it. For me usually 10-12 knights and 2-3 mangonels + the castle are enough to stop that push.
If possible don’t be wasteful with the knights. Picking heavily wounded units and sending them into the castle with herbal medicine or bringing them back to some monks to heal up is another good way to keep your army alive.
Also you can use villagers to repair your mangonels.
You also want to have the ballistics tech at some point for your castle and towers otherwise your castle has real trouble to hit moving enemy units - also get the archer attack upgrades for your TC, towers, castles and of course your ranged units if you use those.
Usually if you defend from one or two strong pushes you should reach imperial age and have quite an economy.
Build another castle towards the enemy - if possible near some gold or stone to secure those ressources for yourself.
If the enemy is rather close to your base you can use that castle as a point to attack the enemy base.
Before reaching imperial age you start building more production buildings to be able to spam army. Get the most important updates for your units as well. Having only 2 or 3 production buildings is a problem when you want to reinforce your dying forces so to overwhelm the enemy you need a good number.
For Paladins I usually want 5-6 in the late game, for halbs at least 5-6 and very late game for spamming them at least 8+, often even far more.
This is to replenish your army as fast as you can since a numbers advantage is huge.
For the attacks you want a castle near the enemy base if that 2nd castle was not yet close enough. If possible build it on a hill - it is a lot stronger up there and takes less damage from attacks from lower ground.
Often to make such a castle you need to also bring your army to defend the villagers building the castle. Bring MANY villagers, 10+ to build it quickly. Some pro’s bring 20+ sometimes to build it fast.
Put all those villagers into the castle as they will add arrows and make the castle fire more deadly. Make sure to have ballistics researched by then + the archer attack upgrades.
The moment the castle is up pull back your defending army under the castle to have the castle fire power help. The AI might try to bring it down with a powerful attack. Try to survive that one and repair the castle if needed with the villagers if they try to treb it down.
If your civ has bombard cannons those are great to snipe trebs attacking your castle. Just keep some units near the BBC to defend them.
You can also heal up your units in the castle. Having 10 archers or hand cannoneers in the castle drastically incrases its damage output. You can also use the other castles for healing your cavalry if there is not enough place in the front one and if you have some time to breath.
Once you have this forward castle secured it’s time to apply some real pressure from the production buildings.
I usually bring at least 2-3 trebs, some rams to soak archer fire and put some pressure on the enemy and a Paladin army to destroy important targets and push into the enemy base when possible - but I retreat them often to heal up unless there is real value to be gained by sacrificing them.
I usually also add my own halbs as soon as the AI starts to spam their own pikes/halbs and keep at least a part of my cav usually alive by sending them back to heal them back up.
Don’t forget to take gold and stone from outside your base where the enemy hasn’t yet been to get more ressources and deny them to the AI.
Since the AI is relentless it can be rough to push through when it plays certain civs. You can just steadily destroy its castles and secure the ground you took by making new castles and push through the enemy base that way until they are weakened enough that you can just overrun them.
If you have opportunities to raid this will make the entire process a lot easier but this approach even works without any raiding.
If you want one of the easier civs for that tactic you can use the Teutons for free murderholes once you reach castle age, free herbal medicine to heal up in castels, double monk heal range, double to garrison space in towers and TC, cheap farms for good eco.
Some of the strongest paladins - just slow, some of the strongest monks, resistance to monk conversions. You can later add faith for a very strong resistance if the AI goes nuts with monks.
Also great siege and 13 range castles with crennelations tech which lets your garrisoned infantry also shoot. Teutonic knights are very fast to tech into and are great to defend against ram pushes or trash spam.
But other civs are very viable too.
If you feel confident enough to do so any early villager kills you can get early game are a huge bonus and will make the game a lot easier.
I also found it rather easy with sicilians. First Crusade for a very cheap faith-level conversion resistance and some free Serjeant Army to spam donjons makes defeating the AI rather easy from my experience.
Add some rams and some light cav or later cavaliers with 8 pierce armor and most AI’s have real trouble.