When Adobe Flash uses the term "Publishing" it does not refer to the publishing, or uploading, of your .swf movie file to an Internet host/server. Flash's "Publishing" is actually only saving your .swf file - the version of your Flash movie that will be displayed in your web page.
Never upload the .fla file to your Internet host/server, only the .swf.
The Flash movies that come with your template already have Publish Settings defined, but in some cases you may want to make a few changes. To do so, open the .fla file in Flash, then go to File in the top menu and choose Publish Settings.
In the Publish Settings window click the Flash tab in the upper left if it is not already selected. In Flash MX the Publish Settings window, with the Flash tab opened, will look similar to this:
When Flash saves your .swf file, it is compressing/optimizing it so it loads as quickly as possible on the Internet. JPEG Quality and Audio Event are two settings which will effect the size of your .swf. The higher the quality, the longer your movie will take to load and appear in your web page.
The settings that have already been defined in your template's Flash movie have been optimized for best quality/least download time, but you may want to experiment and test out the results.
Note: Clicking the Publish button in the upper right of the Publish Settings window saves your .swf into the same folder as the corresponding .fla file. If you do this, you will need to move your new .swf(s) from the fla folder that came with your template package into the html/filled or html/blank folders in order for them to be displayed correctly in your html pages. Your newly saved .swf(s) will replace/overwrite any previous .swf(s) of the same name already present in the html folders.
Upload your .swf files to your Internet host/server just as you would .html and image files. Make sure the .swf(s) are in the same folder as your .html files.
See: Getting Your Template Online
How do I Upload my Website Template Using FTP