You have to do the following in your theme plugin

    // Replace the footer menu item powered
    elgg_unregister_menu_item('footer', 'powered');
    elgg_register_menu_item('footer', ElggMenuItem::factory(array(
        'name' => 'powered',
        'text' => elgg_echo('REPLACEMENT_TEXT'),
        'href' => 'REPLACEMENT_url',
        'title' => elgg_echo('REPLACEMENT_TEXT'),
        'section' => 'meta',
    )));

thank you for the quick response but I do not know what file I need to edit.
This code is certainly useful and I saw several posts but none indicates in which file it should be placed.
Please tell me the name of the file.
Thank you

You need to create your own plugin and place all customizations in there. 

http://learn.elgg.org/en/stable/guides/dont-modify-core.html
http://learn.elgg.org/en/stable/guides/plugins.html

1. I'd rather just modify the existing file of the current theme. This is the version elgg the latest available on the website and I downloaded it there 4 days.

2. Is there a clear manual to install a theme? I searched: http://learn.elgg.org/ but I did not find anything by typing the key words such as: install new theme, install theme etc.

thanks a lot for your help

2. Is there a clear manual to install a theme?

http://learn.elgg.org/en/stable/admin/plugins.html#installation

Try download and activate L1 Theme (simple landing page) for testing on your website

1. Sure, go ahead. Why bother. Why ask for advise from people who have spent the last decade working on Elgg to only do things your own way...

2. Unlike WordPress Elgg doesn't distinguish between themes and plugins. All themes are plugins, all plugins can add theming.

do not be angry , please, I just want a clear explanation so you just give me. I am very thankful to all who work on this project but I can not guess which answer is correct if one replies that he must insert the code without telling me where  and other tell me to do my own plugin. I did not know that Elgg does not distinguish between themes and plugins.

I looked around and there are very few tutorials.

I am not angry. I will be in 3 months when you come back to the forum saying: oops, I made changes to my files, how should I upgrade now without loosing these changes.

"Insert" means create a new plugin where you put all your customizations. This will allow you to upgrade your Elgg version without loosing all the changes you have made. Elgg is pluggable framework, so you can do pretty much everything from within a plugin - don't ever try to "edit" core files.

You need to create one folder with two files to create a plugin: manifest.xml and start.php. Just copy paste the code into start.php. Ideally, put everything into a callback function for the init event.

// start.php

elgg_register_event_handler('init', 'system', function() {

   /**
    * ALL CUSTOMIZATIONS GO HERE
    */
    // Replace the footer menu item powered 
    elgg_unregister_menu_item('footer', 'powered'); 
    elgg_register_menu_item('footer', array( 
       'name' => 'powered', 
       'text' => elgg_echo('REPLACEMENT_TEXT'), 
       'href' => 'REPLACEMENT_url', 
       'title' => elgg_echo('REPLACEMENT_TEXT'), 
       'section' => 'meta', 
    ));
});

Something I put together a long time ago, might help: https://elgg.org/pages/view/830173/tricks-for-elgg-newbies

thank you very much, I'll test it