When starting a project or beginning to look for improvement opportunities to make in to a project, I always recommend capturing the current situation at least within your areas of interest.
Finding the right lane.
Use of a swim lane diagram can be an excellent way to logically break down and layout the flow of a process and the interactions from physical, paperwork and system activities.
Keep it visual.
Keeping this activity visual and practically engaging for a team helps to draw out the required level of detail and interaction.
To start with be clear on what you are trying to understand and why, is it a product, departmental or service process.
Layout a large sheet of paper, I usually like to stick these on a wall for the group to see and add points to as the process grows. Use sticky notes to capture each process step or interaction, this enables you to move things around as additional points or errors are realised which often happens.
Write the departments involved on the left of the sheet and draw horizontal lines above and below each written name to create a lane big enough for the sticky notes to fit in.
The purpose of the exercise is to gather a realistic representation of the process from those involved. It is important to address the team/s involved in the right way ensuring they dont feel judged, trust is established through it being a learning activity and their experience and efforts so far are valued rather than criticised.
It is important along side gathering the process steps and interactions across departments(which may include multiple paths dependant on scenarios) a perspective on time frame is placed against segments of activity.
As you work with the team and layout the points through discussion and questions the real gold can come out of the conversations in between. This is where as steps and activities are played out members will state and outline at length their frustrations and difficulties. You must ensure these are captured either separately or even better I would use a different coloured sticky note to record and highlight these points where they are effective in the process flow.
This can help to work on the process activity further or form a list of future improvement projects and activities.
Treat this as much about Team building and sharing as well as development of improvement opportunities. That trust and engagement is necessary to the future success of the process development and improvement project delivery.
Have fun, enjoy the process and keep it engaging for all. Good Luck!