Once you understand how the computer plays, and what it can't handle, it becomes fairly easy to beat. I lost my first many games of Dominions 1, usually to Ermor. But even when I removed Ermor I still lost. Then I read various strategies and killer combos that people have devised, and I don't think I've ever lost to an AI since... though occasionally there are close calls.
In the base game, there are things you just can't do. Don't recruit slingers, light cavalry, horse archers, militia, or light infantry (some people will argue, but they probably lose to the AI
). Don't spend all your gems on magic items for your ordinary commanders. Don't spend all your gold on conventional armies. Don't rely on archers against heavy armor. Don't fight Ermor or Rlyeh with standard units. Don't summon ice, earth, or fire drakes, or wyverns, or most other low-level summons. Don't buy water mages. Don't set your province defense at 21 everywhere to get the cool new commander. Don't set taxes low to make people happy. In general, don't buy a human pretender. Don't buy any castle other than Castle, Wizard's Tower, Watch Tower, or Fortified City. Don't put a Ring of Water Breathing on a mage, send him underwater, have him build a lab, then put the ring in the lab. Don't make a Holy-2 indy priest into a prophet. Don't send a cyclops into combat, even though they are big and strong, because they have an anime eye that is 90% of their face and always gets hit. Don't use immortals in hostile dominion. Don't take extra paths on a pretender with expensive paths. Don't take Turmoil + Unluck. Don't take Drain unless you are Ulm, then take Drain 3. Don't take Growth either. Don't use Blood mages in battle.
Then there are things that you
do do. Search for magic sites. Spend most of your money on mages, and have them focus their research on a goal. Equip them with Owl Quills, Skull Mentors, and Lightless Lanterns. Never forge anything without a Dwarven Hammer, if your nation can make them. Give Endless Bags of Wine to your commanders of large armies. Buy a Wyrm god and send it out solo on turn one. Or take a Vampire Queen and give it Black Steel Plate and various other items, and let it rip. Mass priests against undead hordes (and by "mass" I mean 20-40, not 2-4). Mass battle-mages aganst normal armies, with Blade Wind, Lightning Bolt, Thunder Strike, Falling Fires, Falling Frost, Nether Bolt, Nether Darts, and so forth. Mass units that don't have upkeep for your armies - Vine Ogres, Summer Lions, Longdeads, Soulless, Fairies, Demons, Vampires, Crossbreeds, and so forth. But get them as cheaply as possible. Go underwater ASAP, using amphibious summons or mercenaries or even an amphibious God. Use boosting items and boosting spells to raise your mage power levels for good combat spells, or to make the spells more powerful and cheaper. Go for spells with multiple effects or wide areas, or ideally, the entire battlefield (Fire Storm, Earthquake, etc). Kill enemy armies remotely with Murdering Winter and similar "artillery" spells. Dedicate 5 provinces to blood-hunting, summon all the Ice Devils, give them nice equipment, and watch them annihilate helpless enemy armies. Or summon Bane Lords, give them Wraith Swords and Flying Boots, and do the same thing. Forge Soul Contracts, Lifelong Protections, and Skullfaces and observe their effects. Mass archers and cast Flaming Arrows and Wind Guide. Research super-strong mass summons and use those instead of low-level single-unit summons; for example, Summon Wights, Ether Gate, Fairy Court, and the mass-Devil, Ice Demon, Storm Demon, and Demon Knight spells. Summon a Lamia Queen to summon Lamias instead of summoning your own Lamias, and summon a Vampire Lord to make Vampires for free instead of summoning Vampires. Summon an Ivy King and give him an Ivy Crown (I forget which slot he's missing... head? hands? feet?), then let him summon Vine Ogres at a huge bonus. If you have a nation with strong holy troops, either pick a strong bless and buy tons of them, or don't use a bless strategy, and don't waste money on sacred units; but don't go half-way.
In general, if you don't do the "don't dos" and pick a few "do dos", you'll beat the AI unless you get encircled by multiple opponents early. You can't just look at it like Risk or Warcraft... you have to plan for
specific long-term killer strategies, then execute them.