What has got in the way so far?
The first activity you will go through together will to discuss the constraints which the team you have just joined have been working under up until now. What technology constraints stop the team from doing the things they want to do, what management constraints exist, what constraints between the team and the wider organisation are stopping the team doing the things it needs to do.
Depending on the size of the team, break up into small groups of two to four people. Spend about 10 minutes with team members in turn sharing amongst their small group their own irritations. The purpose of the initial small group sharing is to give participants an opportunity to test themselves on the significance of their irritation - is the irritation just a personal irritation, or is the irritation one which is indeed preventing the team from moving forward to deliver the best service the team can?
After that initial small group discussion, open the exercise to the floor as a whole. If a team member has an irritation which to them is sufficiently important to share as a significant blocker for the team, then they should write a summary of it onto a sticky note, say their piece to the room, and place their note onto the wall in a place designated for logging the constraints. Then the next person who has something to share takes their turn, etc, until everybody has had the opportunity to say their piece. Don't cram the sticky notes as closely as possible together, leave space around them for later.
People will obviously want to give the context for what they share as a constraint, and other people will obviously want to question them on that; allow them, but try to limit any discussion on it, because the discussion will happen later.
The number of people in the team will obviously affect how much time to spend on this, but if you're still going strong after about 30 minutes then there may be issues more deep-rooted you need to address than can be handled in this session...
This needs to be an honest and frank exercise, but it may not be in the best interests of the team for it to be entirely open. It would be surprising if no team member has an irritation which they may feel concerned about expressing openly - there may issues with how management as a whole is conducted which need airing, but the team member who feels that way may not have sufficient trust that they won't suffer consequences for airing their issue. In advance of the meeting arrange for some way in which a team member can raise such an issue anonymously during the meeting.
After everybody has finished expressing their irritations and posting them to the wall, each person shall take a sheet of six sticky dots, walk over to the wall to admire it, and place their dots next to (not on, because they'll fall off, because you're using budget sticky notes after all) the posted irritations that are important to them; essentially, each team member has six votes to cast - if one irritation is consuming the very fibre of their being, they might place all six of their dots next to it, or they might split their votes between two irritations, three dots each, or whatever.
Try to get a sheet of dots all of the same colour, if you can. You're new to this team, but you've met People before; you know that if the dots are multicoloured folks will ask questions about whether there's any significance to the different colours...
If necessary, you may want to have a separate session to go into an Irritations Audit in more detail.