Sharepoint - How do I create a upload button on SharePoint online

The upload form for a particular library can be accessed from

http://site/_layouts/Upload.aspx?List={ID to the library}

You can get the ID by e.g. going to the Document Library Settings, and the URL should end with List=<ID>. Note, that if the URL starts with %7B and ends with %7D, those are decoded to { and } respectively, meaning you don't have to add the braces to the URL.

When you have your upload URL, you can link it to your desired element such as an image or a text for an upload.