It's easy to render an animation in DAZ Studio. Once you have your animation ready in your scene, go to RENDER –> Render Settings. In the Render Settings Window, look at the lower half. Choose 'Make Movie.' Then below that, you can choose the name and location of the animation.
If you want to render, click on the 'render' button. If you want to render the animation later, click 'Accept' and the settings will be saved, but DAZ Studio will not render.