There are a lot of ways to save actions in Illustrator. You can save them as individual files, or you can save them as part of a group. You can also save them as part of a document, or as a whole file. The best way to save an action is to choose the Save As… option and give it a name. For example, Save As Action1.png. Then, you can use this filename to store the action in your document. If you want to store the action in a group, choose the Group… option and give it a name. For example, Save As ActionsGroup1.png. Then, you can use this filename to store the actions in your document and group them together.