List port mappings or a specific mapping for the container.

docker port CONTAINER [PRIVATE_PORT[/PROTO]]

You can find out all the ports mapped by not specifying a PRIVATE_PORT, or just a specific mapping:

docker ps
CONTAINER ID        IMAGE               COMMAND             CREATED             STATUS              PORTS                                            NAMES
b650456536c7        busybox:latest      top                 54 minutes ago      Up 54 minutes       0.0.0.0:1234->9876/tcp, 0.0.0.0:4321->7890/tcp   test
 
docker port test
7890/tcp -> 0.0.0.0:4321
9876/tcp -> 0.0.0.0:1234
 
docker port test 7890/tcp
0.0.0.0:4321
 
docker port test 7890/udp
2014/06/24 11:53:36 Error: No public port '7890/udp' published for test
 
docker port test 7890
0.0.0.0:4321