I have already googled on this subject and found few threads. Based on these threads I have followed the following steps. But I am facing a problem.

Basically, I want to create a docker image for mysql and then connect to it from my host machine (Mac OS X).

Based on this post , I have to share the mysql unix socket with the host. towards this I have done the following steps

1. Start docker quick terminal
2. docker run --name mysql -e MYSQL_ROOT_PASSWORD=password -d mysql/mysql-server:latest
3. docker exec -it mysql bash
4. mysql -uroot -p
5. create database MyDB;
6. GRANT ALL PRIVILEGES ON *.* TO 'root'@'%' IDENTIFIED BY 'password';
7. exit;
8. mkdir /Users/abhi/host
9. docker run -it -v /host:/shared mysql/mysql-server:latest

Now I get the error

MacBook-Pro:~$ docker run -it -v /Users/abhi/host:/shared mysql/mysql-server
error: database is uninitialized and password option is not specified
  You need to specify one of MYSQL_ROOT_PASSWORD, MYSQL_ALLOW_EMPTY_PASSWORD and MYSQL_RANDOM_ROOT_PASSWORD

But you see that I have provided the password and initialized my database.

All I want is that from my host machine, I can connect to the mysql database running inside docker.

EDIT:: ----- solution which worked ------

Thanks RICO. Finally the steps which worked for me are

1. Start docker quick terminal
2. docker run --name mysql -p 3306:3306 -e MYSQL_ROOT_PASSWORD=password -d mysql/mysql-server:latest
3. docker exec -it mysql bash
4. mysql -uroot -p
5. create database MyDB;
  
  or:
  CREATE USER 'root'@'%' IDENTIFIED BY 'root';
  GRANT ALL PRIVILEGES ON *.* TO 'root'@'%' WITH GRANT OPTION;

6. GRANT ALL PRIVILEGES ON *.* TO 'root'@'%' IDENTIFIED BY 'password';
7. exit;
8. docker-machine env default

Use the IP address obtained in step 8. port is 3306, user is root, password is password, database is MyDB.

Connection is successful!