Go to the Action Group sub-tab on Actions tab, go to needed folder and click New Action Group button (1):

"New Action Group" page will be shown.

Enter the name of new Action group (2).
Set if it is necessary to Track History (3) - when checked, you will be able see the history of action(s) execution.
Enter Description (4) if needed.  

Save. After this an Action Group Details tab will be shown (5):

Click Edit on Action Group View on it's details (6). You can also rename group if Select Edit from list drop-down at the proper entry on groups list (9): 

Execute Button (7) in Action Groups work the same way as for Actions. See more details at Working with existing Action

You can attach a file to the action (e.g., some descriptive document or image). Click "Attach File" button (8) and follow the instructions on the page shown.

Adding existing action to the Action Group.

Click "Add Action" button (10) and Actions tree will be shown in the popup (14). Choose necessary (15) from the list of existing actions:

Adding new action (12) to the action group is the same as adding new action on "Actions" tab. Click "New Action" and refer the article How to create Action to fill in New Action inputs.

Actions in the group will be executed in the specified order (upper first). To change order of actions use "Up" and "Down" links (13).

History tab will show the history of execution of the Action Group if the Track History selected on Action Group properties.

Click View (16) to see details on each action execution:

"Source" cell can contain link to the record for which Action Group ran (if exists).

Variables shows values assigned to the actions from the group.

The toolbar at the top of "Actions Group" page allows to do the following:

• Switch between Actions and Action Groups (17)
• Make search (18) or deep search (19) through Action Groups
• Export selected Action Groups (20) to file
• Import Action Groups (21) from file
• Deploy selected Action Groups (22) to another organization
• Move selected Action Groups and folders (23) to another folder
• Create new Action group (24, see above)
• Click arrow menu (25) to see "New Folder" button that allows to create a new folder.

Action Group, as far as single Action, can have some parameters. In terms of Action Group, parameters can be passed as standard Variables.

The main advantages of Action Group Variables are:

• Variables that are passed as parameters, or defined in some Action in the Group, are available in subsequent Actions.
• These Variables can be changed in the Group with actions of "Define Variable" type.

For example, assume user needs to auto-combine email notification. This can be done with the following way:

1. E.g., user needs to send emails where some person name should be highlighted with given color in all places it appeared.
2. User triggers an Action Group (e.g., by clicking a button on some form) and passes current record creator's ID to this Group as parameter (variable): person = {$SomeObject.SomeUser.Name} and color="purple".
3. first action receives this parameter and updates this variable: person = <span style="background-color:{$Variables.color}; font-weight:bold;padding: 0 0.25em;">{$Variables.person}</span> .
4. second action receives this updated person variable and sends email with some text, like this:

Dear {$Variables.person}, 
We're glad to inform you, that your account "{$Variables.person}" has been upgraded to <b>Pro+</b> plan.
...
Please consult with our online advisors in case of any questions. Type "\" with your account name "{$Variables.person}" in the chat bot message field to get quick assistance.
...

5. In the letter sent all person names will be highlighted.