Hi,
how do I attack other players garrison? I remember from DOS era, that I have to click on enemy military building and sent available troops, but when I do it, there is just message "No attack possible!"

Hey, have you got spare soldiers or enough of the right resources to equip them? What is the objective for the mission, have you been able to attack this enemy before? If its yes to those questions its possible it could be bugged out, restarting the mission might solve that.

if its unlimitied play make sure you havent selected "people vs people" and that your opponent is the same people as you.
And make sure you have many soldiers close enough to the enemy builing, barracks rarely leaves any spear soldiers to fight, guardhouse or watchtower is recommended.
if you have a large land, and no armory/brewery you wil unlikely have enough soldiers to fill up you military buildings close to the border.

Its regular Romain campaign. First mission was without fighting, but I have tried missions 2-4 (those were available since the beginning) so far and I cannot finish them without fighting. All garrisons are full, they are equipped with gold, all is ok. And since this happens in all missions, I really dont know, where the problem is.

Are the garrison buildings near the border of the enemy you wish to attack? You can clear out buildings from the other side of your base and send them over. Also when you want to attack you need to have you men outside the buildings, otherwise they are just guarding your place.

ZFR: Thanks, man! I completely forgot about the army menu. It was in one of those slides.

I really don't understand the mechanics of when you can and can't attack and how many soldiers are available to attack. I'm only on the second mission of the Roman compaign. I have the number of units to attack slider at maximum, but it's never allowed me to select more than 2 units to attack - even when the bordering buildling is a watchtower full with 6 soldiers.
Then in another situation, I had a barracks with 2 generals and the enemy buildling was a guardhouse - I expected I'd be able to send at least 1 general to attack, but I couldn't - it kept saying no attack possible. Are you only able to attack if your available attackers outnumber the defenders?