How to navigate to navigate to another jsff page and then execute a method

Navigation is only for navigation between pages. To subsequently call a method, is not included in navigation, and some automation may need to be performed. If the method call is for unit testing, the automation library may be used.

https://www.oracle.com/corporate/accessibility/templates/t2-10649.html

Call managed bean method on page load. Several blogs on the subject such as "Call method on page load of JSFF (JSF fragment) in Oracle ADF" Also some code snippets:

JSF 1.2 / 2.x

Use @PostConstruct annotated method on a request or view scoped bean. It will be executed after construction and initialization/setting of all managed properties and injected dependencies.

@PostConstruct
public void init() {
    // Do your stuff here.
}

This is strongly recommended over constructor in case you're using a bean management framework which uses proxies, such as CDI, because the constructor may not be called at the times you'd expect it.

JSF 2.0 / 2.1

Use <f:event type="preRenderView"> in case you intend to initialize based on <f:viewParam> too, or when the bean is put in a broader scope than the view scope (which in turn indicates a design problem, but that aside). Otherwise, a @PostConstruct is perfectly fine too.

<f:metadata>
    <f:viewParam name="foo" value="#{bean.foo}" />
    <f:event type="preRenderView" listener="#{bean.onload}" />
</f:metadata>
public void onload() { 
    // Do your stuff here.
}

JSF 2.2+

Alternatively, use <f:viewAction> in case you intend to initialize based on <f:viewParam> too, or when the bean is put in a broader scope than the view scope (which in turn indicates a design problem, but that aside). Otherwise, a @PostConstruct is perfectly fine too.

<f:metadata>
    <f:viewParam name="foo" value="#{bean.foo}" />
    <f:viewAction action="#{bean.onload}" />
</f:metadata>
public void onload() { 
    // Do your stuff here.
}

Note that this can return a String navigation case if necessary. It will be interpreted as a redirect (so you do not need a ?faces-redirect=true here).

public String onload() { 
    // Do your stuff here.
    // ...
    return "some.xhtml";
}

"...I am relatively new to all of this.."

How are the .jsff page fragments used? When you build a JSF page using page fragments, the page can use one or more page fragments that define different portions of the page. The DataControl for the JSF page could be the same.