When you create an asset, Maya arranges the nodes in a number of ways:
You can expand an asset node to display its contents (see Parts of an asset).
In Maya there are two types of assets, and you can interact with each one in different ways.
Assets with transform are simpler and allow direct manipulation and thus are most appropriate for nodes that need to be placed in the scene or the DAG hierarcy (for example, geometry or groups).
Advanced assets are most appropriate for collections of nodes that do not need to interact much with the DAG hierarchy, or for collections of nodes that are not in the same DAG hierarchy (for example, shader networks or character rigs).
In both cases, you add and modify attributes and make attribute connections to asset nodes (and the nodes placed within them) just like you would other nodes in Maya.
For more information on connections, see Connect input and output attributes.