Before we start, you should prepare and import at least two assets containing animations. If you are using a Generic rig, make sure to have the same rig in both assets. You can also use the provided example Unity project and go to the Chapter 01 Working with animationsRecipe 06 Using animations from multiple assets. There is a scene called Example.unity file there. In the scene Hierarchy you can find a Character game object. It has an attached Animator Controller in which you can find two animations: Idle and Wave. In the Rigs directory, you will find the Character.fbx asset containing only a rigged character along with the Idle.fbx and Wave.fbx assets containing the corresponding animations.
If you are exporting FBX files from Blender, make sure to disable the Add Leaf Bones option in the exporter. If you are exporting just the rig and animations (without a mesh), add an empty object to the scene. If you will not do this, your rig could be messed up a bit after import.