JabRef lets you link documents on the web in the form of an URL or a DOI identifier.
Setting up external viewers
JabRef has to know which external viewers to use for web pages. These are by default set to values that probably make sense for your operating system, so there's a fair chance you don't have to change these values.
To change the external viewer settings, go to Options → Preferences → External programs.
Opening external links
There are several ways to open an external web page. In the entry editor, click on the icon "open" right of the text field to open the respective DOI or URL.
In the entry table you can select an entry and use the menu choice, keyboard shortcut or the right-click menu to open the file or web page. Finally, you can click on a URL or DOI icon.
Open DOI via popup
By default the entry table will contain a singly column containing an indicator whether there is a DOI or a URL linked. You can disable any of these in Options → Preferences → Entry table columns.