I'm not sure how others go about it, but this is basically the general order of things I do.
1. I'll brainstorm/storyboard - The most important part for me is a good idea that will keep me interested. A storyboard does not have to be a set design unless otherwise specified (like during build season). On my other projects, I usually just end up writing out different steps with some lengths on them describing what I'll do. Sometimes I'll sketch out what I want things to look like.
2. Modeling - For this step, I usually create a seperate scene for each model, and then later merge them into one. This way modeling isn't slowed down by a massive amount of objects in the scene. I'll usually include textures with this.
3. Compiling - This is where I look at what I have planned and create each scene with everything I need in it (through merging of the objects I've already made).
4. Audio - I would normally include audio in each scene I working with if applicable at this point. This way if I have any cues of when to animate what, I don't have to work off of time and multiplying out my fps.
6. Lighting - Make it look pretty with lights!
5. Animation - This is where I animate everything from simple objects and bipeds to cloth and whatever else I might need to include. If I have a lot of objects, while animating I'll hide what I'm not using or set some to display as box to have it run faster.
6. Effects - Particles is what I would use most often in this step. Some particles I'll put in before the animating if they pretain to the scene, but it doesn't really matter unless it's actually involved in the animation and not just background effect. Other effects usually include things such as fog or lighting effects. Sometimes I'll do this entire step before animating. It doesn't really matter though I guess it could in some situations.
7. Rendering - A lot of the time I'll render in something like 320x280 to make it fast and check for any small problems I have. After that checks out I then end up rendering in something like 720x480 (what can I say? FIRST has got me set on it).
8. Post Processing - Any after effects done in photoshop or another video/audio editor and anything else I want to do with the animation. (Don't use this step for FIRST stuff unless you're using Combustion. They won't like it)
Hope I helped!
