Just double-click and view it in your browser
(you may need to choose the program to use).
Or drag the swf file over and drop it on your browser icon (Chrome, Firefox, Safari.. even IE).
On windows, you can find some files in
Where are some example .swf files on a mac?
The google search link above will give you more ways.
Hit #4 comes from Adobe, so is the 'official' answer, but there are a number of third-party utilities out there that may make playing more convenient.. or save videos to disk, etc.
In many cases, you can't just save a swf file from a website because they may have supplementary files, or allowing playing or website connected only when the swf comes from the website.