To open a file double-click on it. This will download the file (if it's not local yet) and automatically open it up in its native applications.
Double-clicking on an assembly file will automatically download the children parts and then open the assembly in the native application. Any local children parts will not get re-downloaded with the latest version unless you specifically fetch updates or cancel modifications.
Keep in mind, if you open a file this way without checking it out beforehand the file will open in a read only status. If you would like to make changes to the file, check the file out and then open it. This will open the file in a write status, allowing you to make and save changes.