For linking attached files, see File links in JabRef.
JabRef lets you link documents on the web in the form of an URL or a DOI identifier.
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.
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.
By default the entry table will contain a singly column containing an indicator whether there is a DOI or a URL linked. You can remove the "Link identifiers" column in Options → Preferences → Entry table.