This is what I have done and has worked for me.
1. Cool each layer on a wire cake rack.
2. Wrap each layer in plastic wrap. I usually use 2 just to make sure it is completely wrap.
3. Wrap each layer in aluminum foil
4. I then place it in a freezer bag if it fits
5. If I’m freezing more than one cake flavor, I label them.
When I’m ready to use them, I let them thaw while wrapped. I am only a hobby baker so the pros might do it differently.