Just for clarity, Inkscape can't do the animation. Inkscape can only make the images. You have to export a PNG for each "frame", and then use another program to put them together into an animation.
GIMP, which is an open source raster editor, has a simple animation feature. I've used it myself, and found it easy to use. As far as I recall (it's been a long time) I used Import as Layers, to import each "frame" one at a time (as GIMP requires each frame to be on its own layer) (or at least, it did at that time). It was a fairly simple animation, with only about 12 to 15 frames. But if you're making something more complex, you'll probably want something which can handle batch imports.
Over the years, there have been a few different Inkscape extensions which will handle parts of this general process, but I've never tried any of them, so I don't know exactly what all they would do. I don't think any of them did the actual animation, but I don't know for sure. I also don't know if any of them are still working with the current Inkscape version. You can find them at the links Moini gave.
(All the known Inkscape extensions are found in those 3 locations, combined. I'm working on putting them altogether, and on the Home tab here, where they will join the listings of tutorials there now. If nothing else in my life breaks, maybe I'll get it done pretty soon, haha.)
If you could let us know what you learn with your investigation, it would allow us to help others (with more info than what I've been able to give you).
