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Since I was just asked for info on one of my modules and have to do this today.
What you need to do is find out what template is used for the module you wish to add to.
Get a copy of that template, edit the template to include the html, upload the new template overwritting the old one, update the module!
Thats it you should have changed the template and it will display it on the page.
If you wish to edit text, that already exists i.e. submit.php page for links to change your description, edit the langauge/main.php of the module.
This will change as soon as you edit the php and upload it, you don't always need to update the module to see the changes.
Hope that helps, any questions please ask