Depends a bit on the airfields own procedures.
Deicing is usually ordered orally from the ramp agent. At some fields, the deicing crew then brings a form on which one has to indicate the required mixture and areas to be treated, at most fields, this is done via headset or radio (usually on a dedicated deicing frequency) on the deicing pad.
After deicing is completed, the deicing coordinator tells us the deicing code via headset or radio. This contains at least the areas that were treated, the mixture(s) used for this, the starting time of the last step and a confirmation that a post-deicing check (if required, hands-on) has been confirmed.
The deicing staff then notes this information in their paperwork and we note the same in our aircraft log and on the operational flight plan. So there is no need to shut down the engines, open the doors and exchange any papers.