With the characters skinned and rigged I've been animating and animating and animating!
I use a mix of animation methods, but before I do anything I act out the motion with a stop watch. Actually, before I do that I run through the motion or sequence in my mind until I can see the character performing it, then I act it out with a stop watch. This can take a long time, because I stop and write down the number of seconds for each part of the movement so I end up acting it out a number of time. Once I have the timings down, I may roughly sketch the poses in my sketchbook, or I might jump right in to the scene. I also rely a lot on reference material from the web or from real life. I spend a lot of time looking at the movies on gettyimages or the bbc motion gallery. Of course if the scene has sound, I will use the audio as reference.
I usually start with simply animating the position and orientation of the whole character, followed by the hips, then the feet, the upperbody, then the arms and head, working with poses and using next/prev keyframe to check the pose changes. When I think the poses are good I'll do a quick hiddenline render to see it in real time. I usually leave the secondary animation until all the primary animation is done and things are looking good.
I set the fcurves to be created linear by default rather than spline. Of course for things that absolutely need spline curves, I'll switch the curves back to spline immediately. The canary's swing, for example, absolutely needs a spline curve. For all other curves I will decide at the tweaking stage how to edit the curves. For some I will manually set keys to control the ease-in and -outs, for others I'll just switch the curves to spline.
The most unusual thing I've discovered recently is that birds walk in a backwards human tip toe. Take a look at any of the bird quicktime movies on gettyimages and play them backwards, you'll see what I mean.
Rather than re-write what has already been written about animation by those more qualified than myself, here are a number of valuable online animation references:
Character Animation articles from Siggraph
Spline Doctors blog
Keith Lango (blog, short films and tutorials)
Shaun Freeman (collection of animation tips from various sources)
Carlos Baena (collection of animation tips from various sources)
The other things that help me are reference books and videos! I've got the Illusion of Life and the Animator's Survival kit within hand's reach. But nothing starts a good day of animation like watching an animated short (I keep Warner Bros, Pixar, Aardman, and Rocky & Bullwinkle DVDs and tapes close by).