Frankenweenie used stop motion style. This is a classic technique where fgures, such as clay dolls, are moved by a very small amount between frames so that they appear to be moving on their own when the frames are all played on after the other. The very earliest animated films used stop motion, which doesn't need complicated technology, but it is still in use today. Probably the most famous use of clay dolls and stop motion technique is the work of Nick Park, the creator of the Wallace and Gromit films.
One advantage of stop motion is that it is easy to mix with footage of live actors. This can create very striking effects, for example in films like Who Framed Roger Rabbit? Frankenweenie does not use live actors. It is unusual in another way though; it is filmed in 3D, which is very unusual for a stop motion animation.