Welcome to the forum, and to Notepad++.
When editing an HTML file, you don’t just paste it in a browser (like IE or Chrome or Edge or Firefox): you have to open the file in the browser.
If you want to see what your local copy looks like, after saving it in Notepad++, you should be able to go to the menu Run > Launch in IE (or Chrome, Edge, Firefox – this recent post by @Meta-Chuh explains how to add the launch-in-edge to that menu). Alternately, open your browser, and use the File > Open menu (or equivalent – often, Ctrl+O will bring up the Open dialog) to browse your local computer to find the saved HTML file, and open it.
If you want to view it on your webserver, you will have to start by uploading the file to the webserver – you can use an external program like FileZilla, or use the NppFTP plugin for Notepad++. Once it’s on your webserver, then you just need to go to the appropriate URL in your browser of choice.