How to execute a shell script on a remote server using Ansible?

I am planning to execute a shell script on a remote server using Ansible playbook.

blank test.sh file:

touch test.sh

Playbook:

---
- name: Transfer and execute a script.
  hosts: server
  user: test_user
  sudo: yes
  tasks:
     - name: Transfer the script
       copy: src=test.sh dest=/home/test_user mode=0777

     - name: Execute the script
       local_action: command sudo sh /home/test_user/test.sh

When I run the playbook, the transfer successfully occurs but the script is not executed.

local_action runs the command on the local server, not on the servers you specify in hosts parameter.

Change your "Execute the script" task to

- name: Execute the script
  command: sh /home/test_user/test.sh

and it should do it.

You don't need to repeat sudo in the command line because you have defined it already in the playbook.

According to Ansible Intro to Playbooks, user parameter was renamed to remote_user in Ansible 1.4 so you should change it, too

remote_user: test_user

So, the playbook will become:

---
- name: Transfer and execute a script.
  hosts: server
  remote_user: test_user
  sudo: yes
  tasks:
     - name: Transfer the script
       copy: src=test.sh dest=/home/test_user mode=0777

     - name: Execute the script
       command: sh /home/test_user/test.sh