What do you do if you inherit a poorly performing team?

First define what performance metrics are, so we have a clear sense of what is "poor" / "underperforming", then figure out if this is a people problem (e.g. mismatch between skills and outcomes needed) or organization problem (e.g. misalignment of incentives / resources)

Hold individual meetings with team members to learn more.  Build a relationship of trust with each person.  Find out what drives them and learn about the aspirations they have, along with anything holding them back.  Ask the right questions and be willing to listen, asking engaging questions to find out more.  Set some goals and establish some measurables so you can celebrate wins along the way.  Finally, get and make some solid commitments for improvement.  Hold yourself and your team members accountable moving forward.

Try not to make snap judgements.  The team may be doing exactly what their previous manager expected of them.  I've inherited more than my share of teams with management PTSD,  It's not easy.  Take the time to hear them all out individually, and if that doesn't give you the information you need, then do a 360 review with all of them.  The responses can be anonymous.  Find out how they feel about working with each other, and with the company.  Once you think you've narrowed it down, set clear, precise, individual goals that can be discussed during performance reviews, to ensure that you're getting the performance you need.

Great comments below. I agree meeting with them 1 on 1 to assess the situation, their skills, and their ideas on what needs to change is important. In a leadership position, I think it's always important to look in the mirror and ask yourself "what was my role in this?", "what could I have done differently?" In this situation it looks like you inherited the team. Point is, be sure to consider what impact the former leader had on the team. I'm also continually amazed at how much damage one single team member can have on the performance & moral of a team. One person can be a "cancer" in the team. No one wants to work with the person, yet they don't want to be responsible for them being fired. Back to "looking in the mirror", making sure people are in the right seat on the bus or getting them off the bus is the role of leadership (from Good to Great by Jim Collins Jim Collins - Concepts - First Who…Then What?). 

Actions might be
1) Start with 1on1 s to get personal opinions
2) Have team meeting for open discussion
3) Identify the root causes of poor performance altogether
4) Include team in solution identification and roadmap preparation, define measures and milestones for improvement follow up, 
5) Align team members for identified objectives, measures and responsibilities
5) Initiate transformation