What are you trying to do with After Effects? There are so many things that it's hard to point you to one solution. Compositing, motion graphics, text animation, visual effects, image stabilization…
If you want to edit a movie or even a sequence then AE is not the right tool. If you want to create 'shots' that can be edited into a movie or a sequence in a non linear editor, (Premiere Pro, Vegas, Final Cut) then you're looking in the right place.
If you just want to see how AE works try Adobe TV. There are several good overviews of basic workflow and functionality. It's a good place to start.
If you want to do something specific like animating text there's a Search Help field at the top right corner of the app. Type in things like "animate text" or "masking" to be directed to all kinds of resources.
There is a Getting Started Link on the landing page of this forum. Check out that info.
I am looking to get my hands on an instruction manual (a step by step approach on using Adobe After Effects).
Sorry, but If I go by your description, the publication you seek doesn't exist. I don't think it ever has, come to think of it. The closest might be Adobe's Classroom in a Book series for its various applications.
The reason: AE can be used in so many different ways that a manual as the one you describe would be roughly 1/5 the size of an encyclopedia.
Now, there are good links for beginners, and you have them in the above posts, a whole ton of them are free, and I'd take advantage of them.
Check the link above posted by Fuzzy_Barsik, tons of info there...
Message was edited by: Pierre Devereux