It's very simple.
There are the 4 main alliances: Death, Destruction, Order and Chaos. You can play together every model within the same faction using the Grand Alliance rules, as shown in the main rulebook. Then, the models inside the Grand Alliances usually are part of sub-factions, for example Flesh Eater Courts or Nighthaunt. These have their own army rules, if you play only one faction and they are different from the ones in the book. Furthermore, every faction can be "allied" to some of other ones, as shown in the General's Handbook. FEC can't ally with Skeletons for example, but they can do so with zombies or mortarchs.
My advice, if you have just started playing AoS, is to keep it simple: pick the models you or your girlfriend like from Death and play them using only their warscrolls and the rules for Death in the core book. Roll for the traits and relics if you don't know what to pick.
Later you will be able to understand how fragmented AoS rules are, where you can find them and how you can take advantage of all the different possiilities. However, since you are new, I think it's better to do it step-by-step