Genoa in general: Their pros are that they have access to the very famous Italian militias that have bothered many French and HRE players worldwide

On top of that, they have the best xbowmen in the game - and all of these are able to be trained from cities. Genoa has the potential for one of the game's largest economies. Because of this, Genoa can fund and pump out enormous amounts of militia stacks that are reasonably decent (especially with a few armour upgrades). Genoa is by the far the least castle-reliant faction in the game. More cities = more money = more militia stacks.
Field: Utilize your Geonese Crossbowmen. These are by far your best units, and absolutely shine in the field. Keep in mind that they do not work like regular archers (shoot with an arc), but act more like guns (shoot straight line). So keep them in front of your battleline until the moment before impact, then let them retreat behind your melee units. If possible, get them to shoot into the flanks of the enemy - absolutely devastating.
Siege attack: Use siege weapons (trebuchets, catapults, etc) to destroy as many of the towers as possible. Get your men on the walls ASAP to gain control of their towers. The enemy generally retreats to the streets or city square. Get your xbowmen to pump a few volleys into the congested streets or into the mass of soldiers that almost always congregate in the city square. Use infantry as normal.
Siege defense: Your infamous xbowmen are useless here (crossbows can't shoot from walls). Keep spearmen by the gates, and almost any unit on the walls (defending units on the walls get a bonus). If you pin them up at the gates with spearmen, you can get loads of kills from the burning oil from your gates. Also, cannon towers are by far the best building you can have for siege defense. Man all your walls on the front that the enemy is facing, and say goodbye to all their siege weapons and a good 50% of their men.