Personally, I have a rough idea to start out with, but it usual consist of very few colours. I then starting adding extra colours when needed.

 Thanks!  I've got a question: do you figure out all the colors before working on the entire piece, or do you work one element at a time?  I've figured out that my normal way of choosing colors doesn't really work with pixel art.

Some nice stuff in this pic.

At the moment, everything seems to have it's own pallete - so it would be good to mix in the blues from the background with the characters at the front and so on. Working this way would also cut down the amount of colours and make the piece feel a little more tighter. Also, maybe working with just one light source from a given direction, might help with the lighting issue.

The background sky is very nice:)

 Thanks!  You're right, the lighting is a bit off and the animation definitely needs some work.  A lot of this was just trying things out to see how it works.

I agree with Pico. This is actually really good, you seem to understand lighting even though that area could use some work. It also looks like you are familiar with dithering to some degree. The animation is a bit weird, some of his hair pop's up and goes away and there is some twinkling spots on his shoulders -- I don't know if this is suppose to be light reflecting off, if so the rest of the characters should follow suit. The human shouldn't be the only one having light bouncing off of him, if anything the robot creature should be taking that role. This is really good for a first though.

Pretty good for first. Next time try something not that big.