Enclosure Cleaning

What is the proper steps and order of cleaning an enclosure? I have a bottle of Chlorhexidine Solution (2%) that I mix w/ water for disinfecting the cage, hides, etc...

Usually I soak the plastic greenery and climbing grapevine wood structure in a dish soap/water mixture, rinse, spray w/ Chlorhexidine and then rinse again?

Am I doing this correctly and/or recommendations?

Sounds like you've got it covered. I typically spot clean every day. Clean up any new messes. I use kraft paper so I change out the paper with each mess and I disinfect the surface each time also. I change their water supply each morning also

Once every month or so I break down the entire setup and thoroughly disinfect everything from hides, plants, etc.

It sounds to me like you've got a good plan in place.