Ansible: Store command's stdout in new variable?

You have to store the content as a fact:

- set_fact:
    string_to_echo: "{{ command_output.stdout }}"

There's no need to set a fact.

    - shell: cat "hello"
      register: cat_contents

    - shell: echo "I cat hello"
      when: cat_contents.stdout == "hello"

A slight modification beyond @udondan's answer. I like to reuse the registered variable names with the set_fact to help keep the clutter to a minimum.

So if I were to register using the variable, psk, I'd use that same variable name with creating the set_fact.

Example

- name: generate PSK
  shell: openssl rand -base64 48
  register: psk
  delegate_to: 127.0.0.1
  run_once: true

- set_fact: 
    psk={{ psk.stdout }}

- debug: var=psk
  run_once: true

Then when I run it:

$ ansible-playbook -i inventory setup_ipsec.yml

 PLAY                                                                                                                                                                                [all] *************************************************************************************************************************************************************************

 TASK [Gathering                                                                                                                                                                     Facts] *************************************************************************************************************************************************************
 ok: [hostc.mydom.com]
 ok: [hostb.mydom.com]
 ok: [hosta.mydom.com]

 TASK [libreswan : generate                                                                                                                                                          PSK] ****************************************************************************************************************************************************
 changed: [hosta.mydom.com -> 127.0.0.1]

 TASK [libreswan :                                                                                                                                                                   set_fact] ********************************************************************************************************************************************************
 ok: [hosta.mydom.com]
 ok: [hostb.mydom.com]
 ok: [hostc.mydom.com]

 TASK [libreswan :                                                                                                                                                                   debug] ***********************************************************************************************************************************************************
 ok: [hosta.mydom.com] => {
     "psk": "6Tx/4CPBa1xmQ9A6yKi7ifONgoYAXfbo50WXPc1kGcird7u/pVso/vQtz+WdBIvo"
 }

 PLAY                                                                                                                                                                                RECAP *************************************************************************************************************************************************************************
 hosta.mydom.com    : ok=4    changed=1    unreachable=0    failed=0
 hostb.mydom.com    : ok=2    changed=0    unreachable=0    failed=0
 hostc.mydom.com    : ok=2    changed=0    unreachable=0    failed=0