I don't think progress (number of rituals complete) is shared either, so basically designate one person to actually progress and the other person can feed them additional resources when you feel like it. Your plaques are not shared between partners, but you can transfer them to the other. Before you can do those rituals, you need a certain amount of resources (plaques, for the lizardmen).
One thing to keep in mind for overall campaign goals (I'll use the lizardmen as an example because they're what I know): to win the campaign, you need to complete a series of rituals. You can use diplomacy to transfer gold + resources between the two of you. You can't gift units on the campaign map, however. As mentioned in the other comment, if only one army is involved, the commander of that army can (temporarily, for that battle) gift units to the other person. So you can be (for example) two Lizardmen factions, or two Skaven factions, but not one Lizardmen faction and one Skaven faction. One thing to keep in mind is that in Warhammer 2 co-op, the two factions you control both have to be part of the same race.