Get an animation software (ProMotion, GraphicsGale, The Gimp etc.) or build a quick tool that allows you to upload individual frames and then animate them so you can see how the action looks.
Figure out first what kind of action you're trying to make. Don't just try to "animate it" doing something - actually think what you want to do exactly (i.e: attack, jump, dash etc.). Think of the speed this action should have based on the same FPS you use to display your frames inside your game. Imagine your character doing that action and get a feeling of the speed you're going for, and the 'amount of frames' that translates to.
Trace keyframes, which are poses that register the most important points in your action (just the most important points; leave the smoothing-out for the next step). It's very important that they make sense as they are the guidelines. Preview the animation with just these keyframes so you can feel the nature of the action these keyframes represent - if it's not what you wanted originally, revise them.
Trace inbetween frames, which are frames that lie between (duh!) the keyframes and "interpolate" your character's pose from one keyframe to the next. Use as many inbetween frames as necessary so the speeds and motions in this action are realistic, fluid and convincing.
After the action is 'realistic, fluid and convincing', render each frame with production quality.
Refer to Disney's "Animation Principles" every single step of the way while you're doing something like this.