Zymic

Lets begin with choosing an object, Objects-> Primitive-> Sphere, Then you'll get something like this:

Ok now this is done we can make him move around your screen like ..ehh.. a crazy sphere :P. To do this we first need to click on the "Automatic keyframing" button.

So now we can start working on the animation! To do that we need to use the little frame bar under the view screen:

Slide the button to 30 frames (depends on how fast you want the sphere to move) on the frame bar and then move your selected sphere to any place on your screen like i did:

Now you have your first movement.. but you are not finished yet. Slide the button to 60 frames this time (depends on how fast you want the sphere to move) and move your sphere to another place on your screen again. Do it again on 90 frames (depends on how fast you want the sphere to move) but try to put the sphere this time back on the point you started so you will get an smooth animation.

If you are happy with your results, then you can make more objects move at the same time by doing the same as written in this tutorial but with 2 or more objects. If you want to see an example i've made please feel free to download the below .avi video :)