You should aim to meet with 3–4 potential advisors during the first 3 weeks of classes.
First, pick a broad topic, such as income inequality, monetary policy, health, …
Then look for faculty members with expertise in this area. UNC Econ faculty is listed here with their fields of interest. The following is a rough classification:
Look at potential faculty members’ web sites for their working papers and publications. You are looking for someone with an active research agenda.
Schedule appointments with a few potential advisors.
Prepare. Think about potential topics and questions of interest. The more specific you can be, the better.
In your meetings, be concise and precise. Listen.
Do not get discouraged when an advisor “shoots down” your topic. This is normal. Most project ideas are bad. This remains true, even for people who have many years of research experience. See the notes on finding a topic.