Its a bit futile to think of illustrator in the same way as Photoshop. They work differently. The concept of layers in illustrator, is a totally different way of looking at the world.
Anyway do this:
Select the layer. Use the round thing next to the layer name, this selects the layer object. Selecting name activates layer, that is a different thing.
Image 1: Select the layer object (round box next to name)
In the Appearances panel click add new fill (and possibly stroke or expand it with a pathfinder effect)
Image 2: Add new fill
Make the fill the color you want.
Odds are you just want to select all objects and apply a color. Instead of bothering with arcane appearance settings that hardly anybody understands.