This isn't really a guide but more of a summary how the AI acts in skirmish matches and is based on my personal experience from more than 500 hours in singleplayer, mostly playing Annihilation against Normal and Hard AI. Not everything written down here must apply to your own games because the AI behavior differs depending on difficulty level and (sometimes) maps.

But maybe you are new to the game and this helps you to get an edge over the AI.

It appears to me that nobody can say with absolute surety what's the exact differences between the difficulty levels. General consensus is that, starting with normal difficulty, the AI gets a ressource boost that goes up to 200% for Expert AI. Other assumptions are:
- the AI can control more units at the same time and therefore, act on multiple spots of the map simultaniously
- AI units get stat buffs (HP, damage, etc)
- the AI always knows where every enemy unit on the map is, but wont attack them until they come out of the fog of war

What the AI does NOT do is playing smarter or using different tactics. It will just brute force you at higher difficulty levels.

For the campaign, I believe the only difference is that the AI gets hefty stat buffs. More ressources or simultaniously units controlled would be meaningless, since all the campaign missions are mostly scripted.

In skirmish games, you can control the AI to some extent with the "Attack/Defend/Capture here" markers on the minimap. Setting such a marker on the minimap will cause every friendly AI to send all their troops to that point. What marker you use doesn't matter, the AI will always behave the same. It is also possible to send the AI units to a new location by setting a new marker.

However, you can't cancel this command, meaning the AI wont cap points or defend anywhere else on the map, just stay on the point you marked.

It might also happen that the Ai ignores some or all markers you set, but I couldn't figure out a pattern when or why this happens.

• AI can't handle choke points. Bridges, holes in walls, etc. Just set up an MG-nest and a mortar and watch the AI send wave after wave into the death zone.
  
• Ai won't use pioneers or explosives to clear obstacles. You can easily block paths by setting up barbed wire and tank traps.
  
• AI will never build barbed wire, sandbags, tank traps or road blocks. It might use mines near strategic points.
  
• AI rarely builds emplacement like bunkers or MG nests (or trenches as Brits) and when it does, rarely in a good position. Emplacements might even face nonsensical direction. See the units list below for more infos.
  
• AI will never turn neutral buildings into Forward Barracks (with exception of the Panzerelite). It will, however, turn Forward Barracks back into neutral buildings.
  
• AI will never use vehicles to transport units
  
• AI almost never uses unit skills with grenades and Sniper camo being the two big exceptions.
  
• AI will repair damaged vehicles every now and then, including those of human players. They usually repair until the vehicles is back to full health or moves too far away. Damaged AI vehicles wont stop and wait for a player to repair them.
  
• AI wont use unit upgrades that need to be "activated", like the mineflay of the M4 Sherman or the walking Stuka for the Sdkfz 251 Halftrack and the Hotchkiss Light Tank, but it will use "passive" upgrades like .50 cal. gunners or armored skirts.
  
• AI will pick up dropped weapons like Bazookas or LMGs, but wont re-crew heavy machine guns, mortars or AT guns.
  
• AI wont defend its base. For example, even if the Ai holds the majority of the map, building 2-3 tanks and sending them straight to the enemy base is a viable strategy. The AI won't run back to defend but only retreat a few hurt units every know and then.
  
• Ai has problems reinforcing units. Don't be surprised to find a bunch of low life units sitting next to the enemy HQ.

Tinfoil had section:

• AI knows what doctrine you pick and counters it (e.g. you pick Infantry as US, it will spam Snipers)
  
• When playing Bernières-Sur-Mer and Wehrmacht AI gets the inland spawn, it uses nothing but Pioneers and call-in units.
  
• At least on normal difficulty, AI falls off the longer the game goes. If you manage to survive the first 5-10 minutes without falling too far behind, you can turn the game around by dragging it out.

Take this section with a glass of salt. I'm writing this based on my memory alone, I didn't take notes or anything.
The unit selection of the AI depends on game length and available ressources (and maybe the difficulty). I might have never seen some units simply because the games never lasted long enough or because the AI lacked the ressources to use them. It could also be that my brain confuses skirmish games, campaign-mission and matches played in a mod. So yeah, your mileage may vary.
Category explanation:

Always: Expect to see these unit in most of your games.
Sometimes: These units might appear every now and then, but not frequently.
Never: These units basically never get used.
(Obviously, doctrine related units only appear when the AI uses the respective doctrine.)

Always: Engineers, Riflemen, Heavy MG, Mortar Team, M4 Sherman, Rangers, Paratroopers, Paradrop AT Gun
Sometimes: Sniper, AT Gun, Jeep, M8 Armored Car, M4 Sherman Chorodile, M10 Tank Destroyer, Machine Gun Emplacement, Medic Station , Calliope Rocket Launcher
Never: M3 Halftrack, T17 Armored Car, M18 Hellcat, M105 Howitzer, M26 Pershing

Doctrine skills (excluding passive ones and call-in units)
Will use: Off-Map Artillery Support, Supply Drops, Strafing Run, Bombing Run, Field Repairs
Wont use; Air Recon, Raid, Allied War Machine

Always: Volksgrenadiers, Grenadiers, Pioneers, MG42 Team, Mortar Team, Motorcycle, Stug IV, Medic Bunker, Stormtrooper. StuH 42
Sometimes: Sniper, Nebelwerfer, Knight's Cross Holders, Pak 38, Sdkfz 234 Puma, Ostwind, Panzer IV, Panther, MG Bunker, Tiger
Never: Offficer, Goliath, Schwimmwagen, Sdkfz 251 Halftrack, Geschützwagen, Repair Bunker, King Tiger, 88mm Flak

Doctrine skills (excluding passive ones and call-in units)
Will use: Blitzkrieg Assault, Propaganda War, Inspired Assault, Firestorm, For the Fatherland
Wont use; Registered Artillery, 280mm Rocket Artillery, Assault Grenadiers, V1 Rocket Artillery

Always: Infantry Section, Sappers, Bren Carrier, Stuart Light Tank, Lieutenant, Captain, Vickers Machinegun Emplacement, Mortar Emplacement
Sometimes: Cromwell Tank, 17 Pounder AT Gun, Priest Artillery, Commandos, Tetrach tank, Churchill Tank
Never: Staghound Armored Car, Kangaroo Carrier, Sherman Firefly, Cromwell Command Tank, Bofors 40mm Cannon, 25 Pounder Gun Howitzer, HMG Commandos, PIAT Commandos, Mortar Commandos, Churchill AVRE, Churchill Crocodile

Doctrine skills (excluding passive ones and call-in units)
Will use: Decoy Artillery
Wont use; Forward Oberservation Officers, Creeping Barrage, Overwatch Artillery, Counter Battery, Radio Triangulation Detectors, Artillery Strike (from Decoy Artillery), Hull Down

Always: Panzer Grenadiers, Kettenkrad, Scout Car, Mortar Halftrack, Infantry Halftrack, Marder III, Luftwaffe Ground Forces, Hetzer
Sometimes: Tank Busters, Armored Car, Light AT Halftrack, Panzer IV Infantry Support Tank, WIrbelwind
Never: Assault Grenadiers, Schwimmwagen, Munitions Halftrack, Vampire Halftrack, Goliath, Hotchkiss, Bergetiger, Panther, Hummel, Fallschirmjäger, Japdpanther, Flakvierling, 88mm Flak 36

Doctrine skills (excluding passive ones and call-in units)
Will use: Henschel Combat Air Patrol, Teller Mines,
Wont use; Booby Trap Building, Booby Trap Strategic Point, Sector Artillery, Roadblocks, Scorched Earth, Butterfly Bombs