You can use docker top
command. This command lists all processes running within your container.
For instance this command on a single process container on my box displays:
UID PID PPID C STIME TTY TIME CMD
root 14097 13930 0 23:17 pts/6 00:00:00 /bin/bash
All methods mentioned by others are also possible to use but this one should be easiest.
Update:
To simply get the main process id within the container use this command:
docker inspect -f '{{.State.Pid}}' <container id>