The choice of format for animated images make on their own capabilities. Animation formats, GIF and SVG can be created using free programs (respectively, GIMP and Inkscape), while how to get an animated applet of the SWF format have to use a paid software package, Adobe Flash (not to be confused with the free Adobe Flash Player). Also note that viewing animations of the GIF format is possible in almost all browsers, except for some mobile, SWF format only if you've installed Flash Player and SVG - only in modern browsers, mainly for desktop computers.
If you do not wish to create an animated image yourself, use the services of one of the free banks of such images. The animation of the GIF format one can take, for example, on the website AnimatedGifs, SWF - for website Free Flash Animations, and SVG - Wikimedia Commons in the category of Animated SVG. When bringing the images to the public observe the conditions of the license.
For web page animated GIF images, use HTML code similar to that used for inserting static images. If the image is in the same server folder as the HTML file, use this code: <img src=animatedimage.gif>. If ;t it located in another folder on the same server or on another server, will modify code in the following crop <img src=http://site.domain/folder/otherfolder/animatedimage.gif>. Files the SVG format insert in a similar manner, the only difference is that they have a different extension: not a gif, and svg.
Do not try to paste the file in SWF format using the img src tag. This applies to the embed tag, and the code becomes much more cumbersome: <embed src="animatedimage.swf" quality="high" pluginspage="http://www.macromedia.com/go/getflashplayer" type="application/x-shockwave-flash" width="320" height="270" allowScriptAccess="sameDomain" allowFullScreen="True"></embed> where animatedimage.swf name SWF file (or full path), 320 width, 240 height (these numbers can be changed at their discretion).