Once you get past the pleasantries, ask each team member what they think of the current project slate. Are there too many projects or not enough? Which projects do they find interesting? Which ones do they feel are wastes of time?
Take the time to find out how well your team thinks projects have been run in the past. You'll get your best information from the people who actually did the work. Find out what did and did not work.
Find out if your team members understand why some projects were championed and others canceled. This inquiry will show if they understand the sponsor's decision-making process. You'll also learn how far removed team members are from project sponsors (or decision makers).
Dig to see if members "get" what their role is in the implementation of projects. This shows whether they understand how they fit into the project management process and how important they are to the completion of successful projects.
These meetings don't have to be interrogations. Grilling team members with too many questions at once may put them off. Slowly uncovering your team members' perceptions puts you in a better position to refine your approach. You can also gain buy-in for your approach, especially if you've sensed some reluctance to accepting a standardized project management procedure.
When you find out how far removed your team members feel from projects and processes, you'll be able to make an impact right away. By serving as the connection between the project team and the sponsors, you not only position yourself as the "go-to" person for information -- you also become the voice of the project. You can filter information from the sponsors to team members and take team members' feedback to the sponsors.
By doing a little investigating, you may find that it's the first time anyone has listened to the opinions of the team.
And as a new project manager, showing the team that you've heard them will take you a long way.
How have you gotten to know your new team?