I've heard of multiple ways you can tween objects in AS3; I've heard people talking about TweenLite and TweenMax as being the solution to these kinds of problems. However, I'm lost to the whole idea, could someone please explain to me how TweenLite and TweenMax work, and the features they have? If not, could you please link to me a website that offers good information on how to use them effectively?
You have to be a bit careful with the Greensock products. If you plan to use the code for commercial products, you will have to pay for the license. And it is a yearly fee, not a one-time payment.
There are actually free options out there, including tweener (http://code.google.com/p/tweener/) and the tweening that comes with Flash/AS3. Tweener is no longer updated, but still does the job.
Reading the docs or searching for tutorials is the clear first step.